I've been writing a series on Galois Fields / Finite Fields from a computer programmer's perspective. It's essentially the guide that I wanted when I first learned the subject. I imagine it as a guide that could gently onboard anyone that is interested in the subject.

I don't assume too much mathematical background beyond high-school level algebra. However, in some applications (for example: Reed-Solomon), familiarity with Linear Algebra is required.

All code is written in a Literate Programming style. Code is written as reference implementations and I try hard to make implementations understandable.

Currently I've completed the following sections:

01: Group Theory

02: Field Theory

03: Implementing GF(p)

04: Polynomial Arithmetic

05: Polynomial Fields GF(p^k)

06: Implementing GF(p^k)

07: Implementing Binary Fields GF(2^k)

08: Cyclic Redundancy Check (CRC)

09: Linear Algebra over Fields

Future sections are planned:

Reed-Solomon Erasure Coding

AES (Rijndael) Encryption

Rabin Fingerprinting

Extended Euclidean Algorithm

Log and Invlog Tables

Elliptic Curves

Bit-matrix Representations of GF(2^k)

Cauchy Reed-Solomon XOR Codes

Fast Multiplication with FFTs

Vectorization Implementation Techniques

I hope this series is helpful to people out there. Happy to answer any questions and would love to incorporate feedback.