Galois Field arithmetic forms the backbone of erasure-coded storage systems, most famously the Reed-Solomon erasure code. A Galois Field is defined over w-bit words and is termed GF(2^w). As such, the elements of a Galois Field are the integers 0, 1, . . ., 2^w − 1. Galois Field arithmetic defines addition and multiplication over these closed sets of integers in such a way that they work as you would hope they would work. Specifically, every number has a unique multiplicative inverse. Moreover, there is a value, typically the value 2, which has the property that you can enumerate all of the non-zero elements of the field by taking that value to successively higher powers.

This package contains miscellaneous tools for working with gf-complete.