Algebraic Coding Theory

by Elwyn R. Berlekamp

This book concerns state-of-the-art coding and decoding methods. Research reviewed in the book include Berlekamp's algorithm for factoring polynomials (the first significant improvement on a classical mathematical problem in almost two centuries), and Berlekamp's algorithm for decoding Bose- Chaudhuri-Hocquenghem and Reed-Solomon codes. For the past 15 years, this coding algorithm has been used universally in algebraic decoders that correct multiple errors in communications or computer memory systems. Chapters Basic Binary Codes; Arithmetic Operations Modulo an Irreducible Binary Polynomial; The Number of Irreducible q-ary Polynomials of Given Degree; The Factorization of Polynomials Over Finite Fields; The Enumeration of Information Symbols in BCH Codes; appendices and references.

Genres: Mathematics

474 pages, Paperback

First published November 1, 1968

About the author

Elwyn Ralph Berlekamp was a professor emeritus of mathematics and Electrical Engineering and Computer Science at the University of California, Berkeley. He was known for his work in information theory and combinatorial game theory.

Reviews

[Kevin Neilson · Rating 4 out of 5]

There's some good stuff in here, and still relevant today. I learned a sweet trick to do square roots in a Galois Field with just a simple matrix multiplication, and how to find the roots of a Galois quadratic with a simple linear operation. Berlekamp knows his stuff. There are also a lot of circuit diagrams showing how to translate the theory to hardware.

Update: I had a question about a formula and I sent an email to Berlekamp and was surprised to have him write me back. Cool guy! This book has been really useful for helping me design a quintic root solver.

Update: I've been reading more of this book (the original edition) and just want to point out how good it is, especially compared to just about any other textbook in the field. Despite dating to the 60s, there really isn't much about modern error correction circuits that can't be described by this text.

[Qasim Tahir · Rating 5 out of 5]

I want to read this book