Stas,

I don't know how big your matrices are and how you organized your loops,
but I would try the following (written without checking in GAP, so be
careful):

# assuming that n1, n2 and w (integers) are given

f := GF(2);
matrix := NullMat(n1, n2, f); # not sure if this is syntax for null matrix 
                              # over f, check manual
for k in [1..w] do
  i := Random([1..n1]);
  j := Random([1..n2]);
  matrix[i][j] := One(f);
od;

This should run reasonably fast; the expected weight of the matrix is
slightly smaller than the given parameter w, however the error is small
for small weights (quadratic in w/(n1*n2)?).

Hope this helps.
Cheers,
Sven.

--
Sven Reichard
Dept. of Math. Sci.
University of Delaware
reichard@math.udel.edu

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