Hi,
I have attached the output file here. I am sorry that I have not put more
time into cleaning up the code and the output.
Once you figure out what the output is trying to tell you, you will see
that the relevant pairs of strongly regular graphs are isomorphic for dim=4
and dim=6, and also for the first 8 of 10 polynomials for dim=8.
All the best, Paul
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sage: load("boolean_dimension_cayley_graph_classifications.sage")
sage: import cayley_graph_controls as controls
sage: controls.verbose = True
sage: c, reclassification, graph_classes =
load_boolean_dimension_cayley_graph_classifications(2)
1 :
[ 0 1]
[12 4]
Algebraic normal form: x0*x1
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (1, 4, 1, 1))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code and generator matrix for one of the bent functions in the Cayley
class:
Polynomial 2*t^2 + 4*t + 1
Parameters (4, 1, 0, 0)
Rank 4 Order 8
Linear code of length 1, dimension 1 over Finite Field of size 2
Generator matrix:
[1]
Linear code is projective.
Weight distribution {0: 1, 1: 1}
Polynomial t^4 + 4*t^3 + 6*t^2 + 4*t + 1
Parameters False
Rank 4 Order 24
Linear code of length 3, dimension 2 over Finite Field of size 2
Generator matrix:
[1 0 1]
[0 1 1]
Linear code is projective.
Weight distribution {0: 1, 2: 3}
Cayley graph index matrix:
[0 0 0 1]
[0 1 0 0]
[0 0 1 0]
[1 0 0 0]
Weight class matrix:
[0 0 0 1]
[0 1 0 0]
[0 0 1 0]
[1 0 0 0]
sage: c, reclassification, graph_classes =
load_boolean_dimension_cayley_graph_classifications(4)
1 :
[ 0 1]
[160 96]
Algebraic normal form: x0*x1 + x2*x3
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 16, 6, 2))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 8*t^4 + 32*t^3 + 48*t^2 + 16*t + 1
Parameters (16, 6, 2, 2)
Rank 6 Order 1152
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 6, dimension 4 over Finite Field of size 2
Generator matrix:
[1 0 0 0 0 1]
[0 1 0 1 0 0]
[0 0 1 1 0 0]
[0 0 0 0 1 1]
Linear code is projective.
Weight distribution {0: 1, 2: 6, 4: 9}
Polynomial 16*t^5 + 120*t^4 + 160*t^3 + 80*t^2 + 16*t + 1
Parameters (16, 10, 6, 6)
Rank 6 Order 1920
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 10, dimension 4 over Finite Field of size 2
Generator matrix:
[1 0 1 0 1 0 0 1 0 0]
[0 1 1 0 1 1 0 1 1 0]
[0 0 0 1 1 1 0 0 0 1]
[0 0 0 0 0 0 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 4: 5, 6: 10}
Cayley graph index matrix:
[0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0]
[0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1]
[0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1]
[1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1]
[0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1]
[0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0]
[0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0]
[1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1]
[0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0]
[0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0]
[1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0]
[1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1]
[1 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0]
[1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0]
[0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0]
Weight class matrix:
[0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0]
[0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1]
[0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1]
[1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1]
[0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1]
[0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0]
[0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0]
[1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1]
[0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0]
[0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0]
[1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0]
[1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1]
[1 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0]
[1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0]
[0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0]
sage: c, reclassification, graph_classes =
load_boolean_dimension_cayley_graph_classifications(6)
1 :
[ 0 1]
[2304 1792]
Algebraic normal form: x0*x1 + x2*x3 + x4*x5
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 64, 28, 12))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 64*t^8 + 512*t^7 + 1792*t^6 + 3584*t^5 + 5376*t^4 + 3584*t^3 +
896*t^2 + 64*t + 1
Parameters (64, 28, 12, 12)
Rank 8 Order 2580480
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 28, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1]
[0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1]
[0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1]
[0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0]
[0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 35, 12: 28}
Polynomial 2304*t^6 + 13824*t^5 + 19200*t^4 + 7680*t^3 + 1152*t^2 + 64*t + 1
Parameters (64, 36, 20, 20)
Rank 8 Order 3317760
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 36, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1]
[0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1]
[0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1]
[0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 27, 20: 36}
Cayley graph index matrix:
64 x 64 dense matrix over Integer Ring
Weight class matrix:
64 x 64 dense matrix over Integer Ring
2 :
[ 0 2 3]
[ 512 1792 1792]
Algebraic normal form: x0*x1*x2 + x0*x3 + x1*x4 + x2*x5
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 64, 28, 12))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 64*t^8 + 512*t^7 + 1792*t^6 + 3584*t^5 + 5376*t^4 + 3584*t^3 +
896*t^2 + 64*t + 1
Parameters (64, 28, 12, 12)
Rank 8 Order 2580480
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 28, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1]
[0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0]
[0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0]
[0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1]
[0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 35, 12: 28}
Polynomial 256*t^6 + 1536*t^5 + 4352*t^4 + 3584*t^3 + 896*t^2 + 64*t + 1
Parameters (64, 28, 12, 12)
Rank 8 Order 24576
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 28, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1]
[0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 0 1 1]
[0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1]
[0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1]
[0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 35, 12: 28}
Polynomial 192*t^8 + 1536*t^7 + 8960*t^6 + 19968*t^5 + 20224*t^4 + 7680*t^3 +
1152*t^2 + 64*t + 1
Parameters (64, 36, 20, 20)
Rank 8 Order 73728
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 36, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0]
[0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1]
[0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1]
[0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 27, 20: 36}
Cayley graph index matrix:
64 x 64 dense matrix over Integer Ring
Weight class matrix:
64 x 64 dense matrix over Integer Ring
3 :
[ 4 5 6 7]
[1280 768 1024 1024]
Algebraic normal form: x0*x1*x2 + x0*x1 + x0*x3 + x1*x3*x4 + x1*x5 + x2*x4 +
x3*x4
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 64, 28, 12))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 32*t^8 + 256*t^7 + 896*t^6 + 2048*t^5 + 4608*t^4 + 3584*t^3 +
896*t^2 + 64*t + 1
Parameters (64, 28, 12, 12)
Rank 12 Order 6144
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 28, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 1]
[0 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0]
[0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1]
[0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0]
[0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 35, 12: 28}
Polynomial 160*t^8 + 1280*t^7 + 9344*t^6 + 21504*t^5 + 20480*t^4 + 7680*t^3 +
1152*t^2 + 64*t + 1
Parameters (64, 36, 20, 20)
Rank 12 Order 10240
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 36, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 0 1 0]
[0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1]
[0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0]
[0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 27, 20: 36}
Polynomial 64*t^6 + 1024*t^5 + 4096*t^4 + 3584*t^3 + 896*t^2 + 64*t + 1
Parameters (64, 28, 12, 12)
Rank 12 Order 7680
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 28, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0]
[0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0]
[0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1]
[0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0]
[0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 35, 12: 28}
Polynomial 160*t^8 + 1664*t^7 + 9792*t^6 + 21504*t^5 + 20480*t^4 + 7680*t^3 +
1152*t^2 + 64*t + 1
Parameters (64, 36, 20, 20)
Rank 12 Order 7680
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 36, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1]
[0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1]
[0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0]
[0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 27, 20: 36}
Cayley graph index matrix:
64 x 64 dense matrix over Integer Ring
Weight class matrix:
64 x 64 dense matrix over Integer Ring
4 :
[ 8 9 10]
[ 512 1792 1792]
Algebraic normal form: x0*x1*x2 + x0*x3 + x1*x3*x4 + x1*x5 + x2*x3*x5 + x2*x3 +
x2*x4 + x2*x5 + x3*x4 + x3*x5
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 64, 28, 12))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 32*t^8 + 256*t^7 + 896*t^6 + 1792*t^5 + 4480*t^4 + 3584*t^3 +
896*t^2 + 64*t + 1
Parameters (64, 28, 12, 12)
Rank 14 Order 5376
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 28, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0]
[0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0]
[0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 1]
[0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0]
[0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 35, 12: 28}
Polynomial 16*t^8 + 128*t^7 + 448*t^6 + 1280*t^5 + 4224*t^4 + 3584*t^3 +
896*t^2 + 64*t + 1
Parameters (64, 28, 12, 12)
Rank 14 Order 1536
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 28, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 1 0]
[0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1]
[0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0]
[0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1]
[0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 35, 12: 28}
Polynomial 176*t^8 + 1408*t^7 + 9664*t^6 + 22272*t^5 + 20608*t^4 + 7680*t^3 +
1152*t^2 + 64*t + 1
Parameters (64, 36, 20, 20)
Rank 14 Order 1536
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 36, dimension 6 over Finite Field of size 2
Generator matrix:
[1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1]
[0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0]
[0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1]
[0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
Linear code is projective.
Weight distribution {0: 1, 16: 27, 20: 36}
Cayley graph index matrix:
64 x 64 dense matrix over Integer Ring
Weight class matrix:
64 x 64 dense matrix over Integer Ring
sage: c, reclassification, graph_classes =
load_boolean_dimension_cayley_graph_classifications(8)
1 :
[ 0 1]
[34816 30720]
Algebraic normal form: x0*x1 + x2*x3 + x4*x5 + x6*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 245760*t^9 + 3317760*t^8 + 8847360*t^7 + 10321920*t^6 + 6193152*t^5
+ 2007040*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 10 Order 89181388800
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 417792*t^8 + 3342336*t^7 + 11698176*t^6 + 11698176*t^5 + 3760128*t^4
+ 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 10 Order 101072240640
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
2 :
[ 0 2 3 1]
[ 6144 28672 28672 2048]
Algebraic normal form: x0*x1*x2 + x0*x3 + x1*x4 + x2*x5 + x6*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 245760*t^9 + 3317760*t^8 + 8847360*t^7 + 10321920*t^6 + 6193152*t^5
+ 2007040*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 10 Order 89181388800
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 49152*t^9 + 663552*t^8 + 2555904*t^7 + 5079040*t^6 + 4620288*t^5 +
1875968*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 10 Order 56623104
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 327680*t^9 + 4055040*t^8 + 13828096*t^7 + 22183936*t^6 +
14319616*t^5 + 3891200*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 10 Order 94371840
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 417792*t^8 + 3342336*t^7 + 11698176*t^6 + 11698176*t^5 + 3760128*t^4
+ 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 10 Order 101072240640
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
3 :
[ 4 5 6 7 8 9]
[ 6144 2048 16384 16384 12288 12288]
Algebraic normal form: x0*x1*x2 + x0*x6 + x1*x3*x4 + x1*x5 + x2*x3 + x4*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 81920*t^9 + 1368064*t^8 + 4653056*t^7 + 7176192*t^6 + 5406720*t^5 +
1941504*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 12 Order 2097152
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 294912*t^9 + 6299648*t^8 + 21692416*t^7 + 27951104*t^6 +
15630336*t^5 + 3956736*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 12 Order 18874368
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 16384*t^9 + 221184*t^8 + 1277952*t^7 + 3768320*t^6 + 4227072*t^5 +
1843200*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 12 Order 196608
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 262144*t^9 + 4399104*t^8 + 16220160*t^7 + 24281088*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 12 Order 196608
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 49152*t^9 + 729088*t^8 + 2686976*t^7 + 5079040*t^6 + 4620288*t^5 +
1875968*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 12 Order 524288
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 196608*t^9 + 3399680*t^8 + 13172736*t^7 + 21659648*t^6 +
14319616*t^5 + 3891200*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 12 Order 524288
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
4 :
[ 10 11 12 13 14 15]
[15360 9216 16384 16384 5120 3072]
Algebraic normal form: x0*x1*x2 + x0*x2 + x0*x4 + x1*x3*x4 + x1*x5 + x2*x3 +
x6*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 69632*t^9 + 1099776*t^8 + 3784704*t^7 + 6160384*t^6 + 5013504*t^5 +
1908736*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 196608
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 225280*t^9 + 4319232*t^8 + 16203776*t^7 + 24313856*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 327680
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 1536*t^10 + 15360*t^9 + 209920*t^8 + 1280000*t^7 + 3751936*t^6 +
4227072*t^5 + 1843200*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 184320
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 7680*t^10 + 230400*t^9 + 4228096*t^8 + 16058368*t^7 + 24166400*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 184320
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 110592*t^9 + 2344960*t^8 + 10305536*t^7 + 18939904*t^6 +
13664256*t^5 + 3858432*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 589824
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 20480*t^9 + 337920*t^8 + 1556480*t^7 + 3932160*t^6 + 4227072*t^5 +
1843200*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 983040
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
5 :
[ 16 17 18 19 20 21 22 23 24]
[ 4096 6144 6144 2048 2048 6144 6144 16384 16384]
Algebraic normal form: x0*x1*x2 + x0*x6 + x1*x3*x4 + x1*x4 + x1*x5 + x2*x3*x5 +
x2*x4 + x3*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 32768*t^9 + 731136*t^8 + 3096576*t^7 + 5767168*t^6 + 5013504*t^5 +
1908736*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 49152
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 28672*t^9 + 534528*t^8 + 2211840*t^7 + 4718592*t^6 + 4620288*t^5 +
1875968*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 159744*t^9 + 4753408*t^8 + 19021824*t^7 + 26804224*t^6 +
15630336*t^5 + 3956736*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 24576*t^9 + 526336*t^8 + 2342912*t^7 + 4849664*t^6 + 4620288*t^5 +
1875968*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 98304
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 90112*t^9 + 2795520*t^8 + 12402688*t^7 + 21168128*t^6 + 14319616*t^5
+ 3891200*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 98304
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 16384*t^9 + 284672*t^8 + 1392640*t^7 + 3735552*t^6 + 4227072*t^5 +
1843200*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 131072*t^9 + 3577856*t^8 + 15319040*t^7 + 23855104*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 1536*t^10 + 19456*t^9 + 279552*t^8 + 1394688*t^7 + 3751936*t^6 +
4227072*t^5 + 1843200*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 12288
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 5632*t^10 + 148480*t^9 + 3621888*t^8 + 15206400*t^7 + 23773184*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 12288
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
6 :
[ 16 17 18 23 24 19 21 22 20]
[ 4096 6144 6144 16384 16384 2048 6144 6144 2048]
Algebraic normal form: x0*x1*x2 + x0*x2 + x0*x3 + x1*x3*x4 + x1*x6 + x2*x3*x5 +
x2*x4 + x5*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 32768*t^9 + 731136*t^8 + 3096576*t^7 + 5767168*t^6 + 5013504*t^5 +
1908736*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 49152
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 28672*t^9 + 534528*t^8 + 2211840*t^7 + 4718592*t^6 + 4620288*t^5 +
1875968*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 159744*t^9 + 4753408*t^8 + 19021824*t^7 + 26804224*t^6 +
15630336*t^5 + 3956736*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 1536*t^10 + 19456*t^9 + 279552*t^8 + 1394688*t^7 + 3751936*t^6 +
4227072*t^5 + 1843200*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 12288
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 5632*t^10 + 148480*t^9 + 3621888*t^8 + 15206400*t^7 + 23773184*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 12288
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 24576*t^9 + 526336*t^8 + 2342912*t^7 + 4849664*t^6 + 4620288*t^5 +
1875968*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 98304
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 16384*t^9 + 284672*t^8 + 1392640*t^7 + 3735552*t^6 + 4227072*t^5 +
1843200*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 131072*t^9 + 3577856*t^8 + 15319040*t^7 + 23855104*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 90112*t^9 + 2795520*t^8 + 12402688*t^7 + 21168128*t^6 + 14319616*t^5
+ 3891200*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 98304
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
7 :
[ 25 26 27 28 29 30]
[ 6144 21504 21504 2048 7168 7168]
Algebraic normal form: x0*x1*x2 + x0*x1 + x0*x2 + x0*x3 + x1*x3*x4 + x1*x4 +
x1*x5 + x2*x3*x5 + x2*x4 + x6*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 29696*t^9 + 655360*t^8 + 2789376*t^7 + 5332992*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 43008
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 20480*t^9 + 409600*t^8 + 1837056*t^7 + 4235264*t^6 + 4423680*t^5 +
1859584*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 12288
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 143360*t^9 + 3981312*t^8 + 16697344*t^7 + 25108480*t^6 +
15302656*t^5 + 3940352*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 12288
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 64512*t^9 + 2316288*t^8 + 10932224*t^7 + 19783680*t^6 + 13991936*t^5
+ 3874816*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 129024
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 92160*t^9 + 2979840*t^8 + 13608960*t^7 + 22388736*t^6 + 14647296*t^5
+ 3907584*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 36864
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 6144*t^9 + 124928*t^8 + 944128*t^7 + 3219456*t^6 + 4030464*t^5 +
1826816*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 36864
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
8 :
[ 31 32 33 34 35 36]
[ 6144 4096 4096 2048 24576 24576]
Algebraic normal form: x0*x1*x2 + x0*x5 + x1*x3*x4 + x1*x6 + x2*x3*x5 + x2*x4 +
x3*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 32768*t^9 + 712704*t^8 + 3014656*t^7 + 5734400*t^6 + 5013504*t^5 +
1908736*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 131072
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 24576*t^9 + 466944*t^8 + 2064384*t^7 + 4685824*t^6 + 4620288*t^5 +
1875968*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 393216
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 172032*t^9 + 5332992*t^8 + 20283392*t^7 + 27295744*t^6 +
15630336*t^5 + 3956736*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 393216
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 147456*t^9 + 3858432*t^8 + 15990784*t^7 + 24150016*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 393216
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 16384*t^9 + 270336*t^8 + 1376256*t^7 + 3768320*t^6 + 4227072*t^5 +
1843200*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 163840*t^9 + 3858432*t^8 + 15532032*t^7 + 23887872*t^6 +
14974976*t^5 + 3923968*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 14 Order 32768
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
9 :
[ 37 38 39 40 41 42 43 44]
[9216 7168 8192 8192 8192 8192 9216 7168]
Algebraic normal form: x0*x1*x6 + x0*x3 + x1*x4 + x2*x3*x6 + x2*x5 + x3*x4 +
x4*x5*x6 + x6*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 45056*t^9 + 780288*t^8 + 2998272*t^7 + 5505024*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 229376
Polynomial 45056*t^9 + 780288*t^8 + 2998272*t^7 + 5505024*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 229376
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 184320*t^9 + 3852288*t^8 + 14893056*t^7 + 23003136*t^6 +
14647296*t^5 + 3907584*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 294912
Polynomial 184320*t^9 + 3852288*t^8 + 14893056*t^7 + 23003136*t^6 +
14647296*t^5 + 3907584*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 294912
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 105984*t^8 + 976896*t^7 + 3440640*t^6 + 4128768*t^5 + 1835008*t^4 +
286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 258048
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 9216*t^10 + 264192*t^9 + 4468224*t^8 + 16803840*t^7 + 24772608*t^6 +
15138816*t^5 + 3932160*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 258048
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 9216*t^9 + 124416*t^8 + 976896*t^7 + 3440640*t^6 + 4128768*t^5 +
1835008*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 258048
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 193536*t^9 + 4449792*t^8 + 16803840*t^7 + 24772608*t^6 +
15138816*t^5 + 3932160*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 258048
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 45056*t^9 + 780288*t^8 + 2998272*t^7 + 5505024*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 229376
Polynomial 45056*t^9 + 780288*t^8 + 2998272*t^7 + 5505024*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 229376
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 184320*t^9 + 3852288*t^8 + 14893056*t^7 + 23003136*t^6 +
14647296*t^5 + 3907584*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 294912
Polynomial 184320*t^9 + 3852288*t^8 + 14893056*t^7 + 23003136*t^6 +
14647296*t^5 + 3907584*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 294912
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
10 :
[ 45 46 47 48 49 50 51 52 53 54]
[2048 7168 7168 8192 8192 8192 8192 2048 7168 7168]
Algebraic normal form: x0*x1*x2 + x0*x3*x6 + x0*x4 + x0*x5 + x1*x3*x4 + x1*x6 +
x2*x3*x5 + x2*x4 + x3*x7
Function is bent.
Dillon-Schatz incidence structure t-design parameters: (True, (2, 256, 120, 56))
Clique polynomial, strongly regular parameters, rank, and order of each
representative Cayley graph in the extended affine class;
linear code, generator matrix, and corresponding clique polynomial, strongly
regular parameters, rank, and order for one of the bent functions in the Cayley
class:
Polynomial 16384*t^9 + 464896*t^8 + 2310144*t^7 + 5046272*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 114688
Polynomial 16384*t^9 + 464896*t^8 + 2310144*t^7 + 5046272*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 114688
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 12288*t^9 + 301056*t^8 + 1589248*t^7 + 4128768*t^6 + 4423680*t^5 +
1859584*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 32768
Polynomial 12288*t^9 + 301056*t^8 + 1589248*t^7 + 4128768*t^6 + 4423680*t^5 +
1859584*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 32768
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 110592*t^9 + 4159488*t^8 + 17285120*t^7 + 25296896*t^6 +
15302656*t^5 + 3940352*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 32768
Polynomial 110592*t^9 + 4159488*t^8 + 17285120*t^7 + 25296896*t^6 +
15302656*t^5 + 3940352*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 32768
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 2048*t^9 + 167424*t^8 + 1091584*t^7 + 3440640*t^6 + 4128768*t^5 +
1835008*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 28672
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 7168*t^10 + 143360*t^9 + 3804672*t^8 + 15886336*t^7 + 24313856*t^6 +
15138816*t^5 + 3932160*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 28672
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 9216*t^9 + 181760*t^8 + 1091584*t^7 + 3440640*t^6 + 4128768*t^5 +
1835008*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 28672
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 107520*t^9 + 3790336*t^8 + 15886336*t^7 + 24313856*t^6 +
15138816*t^5 + 3932160*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 28672
Strongly regular graph from code is isomorphic to Cayley graph.
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 16384*t^9 + 464896*t^8 + 2310144*t^7 + 5046272*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 114688
Polynomial 16384*t^9 + 464896*t^8 + 2310144*t^7 + 5046272*t^6 + 4816896*t^5 +
1892352*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 114688
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Polynomial 110592*t^9 + 4159488*t^8 + 17285120*t^7 + 25296896*t^6 +
15302656*t^5 + 3940352*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 32768
Polynomial 110592*t^9 + 4159488*t^8 + 17285120*t^7 + 25296896*t^6 +
15302656*t^5 + 3940352*t^4 + 417792*t^3 + 17408*t^2 + 256*t + 1
Parameters (256, 136, 72, 72)
Rank 16 Order 32768
Linear code of length 136, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 136 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 64: 119, 72: 136}
Polynomial 12288*t^9 + 301056*t^8 + 1589248*t^7 + 4128768*t^6 + 4423680*t^5 +
1859584*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 32768
Polynomial 12288*t^9 + 301056*t^8 + 1589248*t^7 + 4128768*t^6 + 4423680*t^5 +
1859584*t^4 + 286720*t^3 + 15360*t^2 + 256*t + 1
Parameters (256, 120, 56, 56)
Rank 16 Order 32768
Linear code of length 120, dimension 8 over Finite Field of size 2
Generator matrix:
8 x 120 dense matrix over Finite Field of size 2
Linear code is projective.
Weight distribution {0: 1, 56: 120, 64: 135}
Cayley graph index matrix:
256 x 256 dense matrix over Integer Ring
Weight class matrix:
256 x 256 dense matrix over Integer Ring
