It is a bit surprising that the communications toolbox provides functionality for elements over gf(2), but it does not provide functionality for finding the null space of a matrix over the Galois field. These two files are simple modifications of the standard files "null.m" and "rref.m". The modification finds the null space of a matrix over gf(2).
This script does not work, I was able to reproduce the same problem mentioned by Eliran Avni, this script gives the wrong result for the matrix [1 1 0; 1 0 1; 0 1 1], for example.
Did you test your script on aaa = [1 1 0 ; 1 0 1 ; 0 1 1]?
Over Z_2, these vector are linearly dependent, and the matrix has a non trivial vector in its null space - [1 1 1].
Yet, gfnull(aaa) returns an empty matrix (at least, when I run it).
in the file gfrref.m, please remove A=gf(A,2). This converts A to GF(2^2).
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