Matlab: rank of a matrix in GF(2)?

From: Jaco Versfeld (jaco_versfeld_at_hotmail.com)
Date: 06/14/04 

Date: 14 Jun 2004 07:11:22 -0700

Hi,

I have cross-posted this to different groups, I thought that it would
be relevant to all, if not please let me know.

I have a matrix consisting of the identity matrix and some other
matrix, i.e. my matrix has the form H = [I L], where the elements are
in GF(2).

Actually, I have a binary code which is generated by a generator
matrix G. G is in systematic form, so that G can be written as G = [P
I], where I is the (k X k) identity matrix. Relating this to the
above, I compute the transpose of P in the generator matrix G, and use
that as my matrix L. With this, the matrix H should be a parity-check
matrix of the code generated by G.

There is a theorem stating that the minimum distance of the code can
be derived by observing the minimum amount of columns of H that can be
added together that gives the zero vector.

Is this the same as computing the rank of the transpose of H?

I have tried to verify the above with a matrix H in Matlab using
gfrank, but Matlab only returned the dimension of the identity matrix
I of H (I is the ((n-k)X (n-k)) identity matrix), which was not the
minimum distance of the code. Is this a bug with gfrank? How can I
determine the rank of a matrix?

Any suggestions, help and/or pointers to literature will be greatly
appreciated
Jaco

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