On Apr 15, 8:45 am, Andrea Gobbi <[email protected]> wrote:
> Hi!
> I'm using sage for coding theory, and it sems to be great! I have a
> linear code like this:
> MS = MatrixSpace(GF(3),10,27)
> G = MS([
> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
> [1,2,0,0,0,0,1,1,2,2,0,0,0,0,1,1,2,2,1,1,1,1,2,2,2,2,0],
> [0,0,1,2,0,0,1,2,1,2,1,1,2,2,0,0,0,0,1,1,2,2,1,1,2,2,0],
> [0,0,0,0,1,2,0,0,0,0,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,0],
> [0,0,0,0,0,0,1,2,2,1,0,0,0,0,0,0,0,0,1,1,2,2,2,2,1,1,0],
> [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,1,1,2,1,2,2,1,2,1,0],
> [0,0,0,0,0,0,0,0,0,0,1,2,2,1,0,0,0,0,1,2,2,1,1,2,2,1,0],
> [1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0],
> [0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0],
> [0,0,0,0,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0]]);
> C = LinearCode(G);
> C.dimension();
> C.length();
> C.minimum_distance();
> C.weight_distribution();
> And I want use the minimum distance (in this case 9) for correct a
> vector with 8 erasures. There are some tools in sage to do this? I try
> to look to the reference manual but seems that the decoding part is
> not implemented...
> Or someone created a soubrutine that can be used for this problem?
> Sorry for my english,
> Thanks!
The following seems to be working,
def decode(w,erasures=[],num_tries=10):
pos=[i for i in range(27) if not i in erasures]
G1=G.matrix_from_columns(pos)
if G1.rank()!=10:
print "Too many erasures"
return None
else:
MH=MatrixSpace(GF(3),G1.ncols(),10)
for i in range(num_tries):
R=MH.random_element()
H=G1*R
if H.rank()==10:
break
return vector(GF(3),w.list_from_positions(pos))*R*H.inverse()
For example,
m=V.random_element(); m
(2, 1, 0, 0, 1, 2, 0, 1, 0, 0)
w=m*G; w
(1, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 1, 1, 0,
2, 1, 2, 0,
1, 2, 2)
decode(w)
(2, 1, 0, 0, 1, 2, 0, 1, 0, 0)
decode(w, range(8))
(2, 1, 0, 0, 1, 2, 0, 1, 0, 0)
decode(w,range(15))
Too many erasures
Alec Mihailovs
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