I'm working on the Gaussian elimination being implemented on gf(2). I have successfully reduced my 286*286 matrix into rref. Now I need to find the null space of this(please tell me how to do this effectively as I'm going to hardcode this in java). It would be a great help is someone could give me the gist of finding basis and then solution of this. Also as a extra detail I'm doing all this as a part of my attempt to implement Quadratic Sieve in java.