I have a sparse binary matrices whose properties I want to analyze over the binary field. The application is to analyze some sparse, binary error-correcting codes. The matrices themselves are too big to handle as full dense matrices, with sizes on the order of 10,000 x 30,000 and bigger, even though only a small percentange of entries are going to be filled. I want to be able to do binary linear algebra while exploiting the matrices' sparsity.
The two main things I will need to do are:
-finding a basis of intersection of its row space with the row space of another sparse matrix
-finding its rank
I've seen that there some packages to find subspace intersection (e.g. this MuPAD function) and to find the rank of a matrix over different fields (like gfrank), but they take prohibitively long time for the matrices I'm working with.
Is there anything like this available? Or any tricks that can be used to do this? If this is possible in another programming language that would also be helpful.
