Dear group members,
I have the following question. Suppose I have one
non square matrix(i.e. *generator matrix of some linear code over finite
field with 2 elements*)over GF(2), whose rows will span one particular
vector space say V or linear code over GF(2).
G=G=matrix(GF(2),[[1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1],
[0,1,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0],
[0,0,1,0,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1],
[0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0],
[0,0,0,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0]])
Call each of the row as a,b,c,d,e as follows:
a=[1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1];
b=[0,1,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0];
c=[0,0,1,0,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1]
d=[0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
e=[0,0,0,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0]
Now define a norm of a subcode/subspace as:
If D is a subcode of C/subspace of V, then norm of D is defined as:
* norm of D = | {i ∈ {1, . . . , n} : there exists v ∈ D with vi is
non-zero} |. *
e.g. If D={(0,0,0),(1,0,0),(0,1,0),(1,1,0)} which is vector space/linear
code over GF(2), then norm of D=|{1,2}|=2
Then if I take a linear span of any two distinct vectors from above matrix,
then I will get 10 (since there are 5 choose 2 choices for this) two
dimensional subspaces/subcodes of V or C.
*My question is how to find number of subspaces/subcodes in this vector
space/linear code of dimension two and given norm(i.e.of varying norm from
1,2,...at the most 19 in above example of matrix G) using sage?*
--
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Yours faithfully,
-----------------------------------------------------------------------
*Mr. Nitin Shridhar Darkunde.Assistant Professor,Department of
Mathematics,School of Mathematical Sciences,Swami Ramanand Teerth
Marathwada University,Vishnupuri, Nanded-431 606 (M.S.), India.Mob.
No:08275268895 Or
09273500312*********************************************************
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