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?* -- ---------------------------------------------------------------------- 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********************************************************* -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.