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(2w). 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.

• Ilya Kurdyukov
• Alexey Shabalin

• gf-complete-tools
• gf-complete-tools-debuginfo
• libgf-complete
• libgf-complete-debuginfo
• libgf-complete-devel