#10153: Canonical generator matrices for linear codes and their automorphism
groups
------------------------------+---------------------------------------------
Reporter: tfeulner | Owner: wdj
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7
Component: coding theory | Keywords: Automorpism group, canonical
representative
Author: Thomas Feulner | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
------------------------------+---------------------------------------------
Comment(by wdj):
Installed fine on a 10.6.6 mac running 4.7.a1. However, there was the
following doctest failure:
{{{
sage -t -force_lib "devel/sage/sage/coding/code_can.pyx"
**********************************************************************
File
"/Volumes/Bay2/sagefiles2/sage-4.7.alpha1/devel/sage/sage/coding/code_can.pyx",
line 495:
sage: canonizer._latex_()
Expected:
'\\textnormal{Canonization object for linear codes over finite fields
or } `\\ZZ_4`\\textnormal{. The actual code is generated
by}\\\\\\left(\\begin{array}{rrrrrrr}\n1 & 0 & 0 & 1 & 0 & 1 & 0 \\\\\n0 &
1 & 0 & 1 & 0 & 1 & 1 \\\\\n0 & 0 & 1 & 1 & 0 & 0 & 1 \\\\\n0 & 0 & 0 & 0
& 1 & 1 & 1\n\\end{array}\\right)'
Got:
'\\textnormal{Canonization object for linear codes over finite fields
or } `\\ZZ_4`\\textnormal{. The actual code is generated
by}\\\\\\left(\\begin{array}{rrrrrrr}\n1 & 0 & 0 & 0 & 0 & 1 & 1 \\\\\n0 &
1 & 0 & 0 & 1 & 0 & 1 \\\\\n0 & 0 & 1 & 0 & 1 & 1 & 0 \\\\\n0 & 0 & 0 & 1
& 1 & 1 & 1\n\\end{array}\\right)'
**********************************************************************
File
"/Volumes/Bay2/sagefiles2/sage-4.7.alpha1/devel/sage/sage/coding/code_can.pyx",
line 358:
sage: [a[0] * Gamma.apply_morphism(a[2]) * a[1] == Gamma for a in
gens]
Expected:
[True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True]
Got:
[True, True, True, True, True, True, True, True, True, True, True,
True, True, True]
**********************************************************************
File
"/Volumes/Bay2/sagefiles2/sage-4.7.alpha1/devel/sage/sage/coding/code_can.pyx",
line 476:
sage: repr(canonizer)
Expected:
'Canonization object for linear codes over finite fields or `\\ZZ_4`.
The actual code is generated by\n[1 0 0 1 0 1 0]\n[0 1 0 1 0 1 1]\n[0 0 1
1 0 0 1]\n[0 0 0 0 1 1 1]'
Got:
'Canonization object for linear codes over finite fields or `\\ZZ_4`.
The actual code is generated by\n[1 0 0 0 0 1 1]\n[0 1 0 0 1 0 1]\n[0 0 1
0 1 1 0]\n[0 0 0 1 1 1 1]'
**********************************************************************
3 items had failures:
1 of 7 in __main__.example_10
1 of 44 in __main__.example_6
1 of 7 in __main__.example_9
***Test Failed*** 3 failures.
For whitespace errors, see the file
/Users/davidjoyner/.sage//tmp/.doctest_code_can.py
[43.1 s]
----------------------------------------------------------------------
The following tests failed:
sage -t -force_lib "devel/sage/sage/coding/code_can.pyx"
Total time for all tests: 43.2 seconds
}}}
Honestly, I'm not sure the best way of returning the component of the
automorphism group which corresponds to field automorohisms. Sage does not
seem to have the Galois action on a vector space such as GF(4,"a")^3
implemented. You can try to return an element of this component as a tuple
of integers which give the exponents of a Frobenius action. You might also
just return it as a separate abelian group. There are probably other ideas
out there too. How does Magma do it?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10153#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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