[wdevanny]

I was thinking along the same lines when the systems of linear equations came up. The difficulty is that the variables are 0-1 while the equations are over the integers. So this is not quite as simple as solving a system over F_2, but is instead feasibility testing of an IP with 0-1 variables and a 0-1 matrix.

I wonder if solving the LP-relaxation might lead to a rounding based approach.