How can I solve the sparse linear system with the coefficients in Z_2?

I want to solve a large sparse linear equation systems with coefficients in Z_2 using Eigen. First we have tried the Boolean type which does not work because 1+1=1 in Boolean but I expect 1+1=0. Hence a solution might be a new customised scalar type. But how it works exactly? Some suggestions of other packages or software are also welcome.