Algorithm to calculate rref in GF(2)?

Question

I have a matrix :: [[Int]] whose elements are all either zero or one.

How can I efficiently implement rref in GF(2)?

_{If LU decomposition can be used to calculate rref(matrix) in GF(2), any example or elaboration on the algorithm would be greatly appreciated.}

Answer 1

1. I don't think it's possible to make an efficient GF(2) implementation using hmatrix, it was designed to handle "big" numbers, not bits.

2. You definitely don't want to use a Double to encode a Bit, that's 64 times more memory than what you actually need.

3. Have you searched for rref algorithms that are optimized for GF(2) ? A generic Gaussian elimination or LU decomposition might not be the best solution in GF(2).