Learn You Galois Fields for Great Good
Hi All, 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…
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Hi All, 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.
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