Learn you Galois Fields for Great Good
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Table of Contents
This is the Table of Contents to a series on Abstract Algebra. You can dive into the introduction here.
Chapters
- 00: Introduction
- 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
- 10: Reed-Solomon as Polynomial Representation
- 11: Reed-Solomon as Linear Algebra
- 12: Reed-Solomon as Discrete Fourier Transform
- 13: AES (Rijndael) Encryption
Backlog of Possible Future Topics:
- Reed-Solomon as BCH Code
- Rabin Fingerprinting
- Extended Euclidean Algorithm
- Log and Invlog Tables
- Elliptic Curves
- Bit-matrix Representations
- Fast Multiplication with FFTs
- Vectorization Implementation Techniques