Reduction of Huge, Sparse Matrices over Finite Fields Via Created Catastrophes

Carl Pomerance J. W. Smith

Abstract

We present a heuristic method for the reduction modulo 2 of a large, sparse bit matrix to a smaller, dense bit matrix that can then be solved by conventional means, such as Gaussian elimination. This method worked effectively for us in reducing matrices as large as 100,000 × 100,000 to much smaller, but denser square matrices.