ALGEBRAIC CODING THEORY

by Elwyn R. Berlekamp

This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.

Genres: Mathematics

474 pages, Hardcover

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