All I need for using regular tools for simultaneous linear equations is a field, right? And {0, 1} with addition modulo 2 and xor is a field, isn’t it? It seems to me it’s just regular Z_2 arithmetics, but it’s a bit too Monday to check.

I want to solve up to 128 equations with 128 unknowns of the form

\sum_{0 \leq i < 128} a_{i,j} xor x_i = b_j 0 \leq j < 128 with a_{i,j},b_j \in {0, 1}

I don’t have to be smart, do I? I can just blindly implement row reduction?