Hi All,<p>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.<p>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.<p>All code is written in a Literate Programming style. Code is written as reference implementations and I try hard to make implementations understandable.<p>Currently I've completed the following sections:<p>01: Group Theory<p>02: Field Theory<p>03: Implementing GF(p)<p>04: Polynomial Arithmetic<p>05: Polynomial Fields GF(p^k)<p>06: Implementing GF(p^k)<p>07: Implementing Binary Fields GF(2^k)<p>08: Cyclic Redundancy Check (CRC)<p>09: Linear Algebra over Fields<p>Future sections are planned:<p>Reed-Solomon Erasure Coding<p>AES (Rijndael) Encryption<p>Rabin Fingerprinting<p>Extended Euclidean Algorithm<p>Log and Invlog Tables<p>Elliptic Curves<p>Bit-matrix Representations of GF(2^k)<p>Cauchy Reed-Solomon XOR Codes<p>Fast Multiplication with FFTs<p>Vectorization Implementation Techniques<p>I hope this series is helpful to people out there. Happy to answer any questions and would love to incorporate feedback.