> < ^ Date: Tue, 07 Dec 1999 13:39:21 +1100 (EST)
< ^ From: Chris Charnes <charnes@uow.edu.au >
^ Subject: Row reducing (0,1) matrices over finite fields (fwd)

Dear gap forum

----- Forwarded message from Ken W. Smith -----

Dear Forum,
I've been using GAP to create incidence matrices of combinatorial
designs. (An incidence matrix M has entries which are 0 and 1 and so the
matrix may be viewed as existing over *any* field.) I would now like to
examine the codes generated by these matrices, that is, I would like to
examine the row space of the matrix M over a field of prime order. I'd
like to find bases for the row space.
How do I do this? A first step, I assume, is to row reduce the
matrix M mod p, but I can't seem to find the right commands.

Thanks in advance,

Ken W. Smith, Professor of Mathematics, Central Michigan University

----- Forwarded message from Ken W. Smith -----

The Guava command
C:= GeneratorMatCode( M, <F> ), F = GF(p),
will create a code record with M as the generator matrix.
The information you require is contained in this record.
The weight enumerator and other properties of C can then be computed.

Chris Charnes

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