### Solve large system of linear equations over GF(2)

I need to solve a pretty large system of linear equations over GF(2) (The matrix is around 20000 x 20000). The straightforward approach used to solve linear equation systems (by using MatrixSpace and octave) will ran out of memory before even building up the matrix.

I wonder if there is any method i could use to solve such a system. Also note that the system i try to solve is sparse in general.