Technical Notes

Introduction

There isn’t a lot of material on the web devoted to computational work in GF(2).
We add some here:

Paper	Topic
Working in GF(2)	Some notes about the vagaries of working in \(\mathbb{F}_2\).
Library Design Notes	Notes about the overall design of the bit library.
Danilevsky’s Method	An algorithm to compute the characteristic polynomial of a square matrix — the algorithm isn’t well known, so we review it here.
Polynomial Reduction	An algorithm to compute \(x^N\) mod \(P(x)\) where \(P(x)\) is a polynomial over \(\mathbb{F}_2\) and \(N\) is potentially a huge integer.