There isn't a lot of material on the web devoted to computational work in bit-space.

This section collects some notes that may be of interest to users of the gf2 library

Paper	Topic
Working in GF(2)	Some notes about the vagaries of working in \(\mathbb{F}_2\).
Danilevsky's Method	An algorithm to compute the characteristic polynomial of a square matrix.
Modular Reduction	An algorithm to compute \(x^N \bmod{P(x)}\) where \(P(x)\) is a polynomial over \(\mathbb{F}_2\).