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.

Algebraic Coding Theory (Systems Science)

Science & Math

Berlekamp, Elwyn

Mathematics

McGraw-Hill Book Company

In this unique book, the authors, both only amateur Go players themselves, develop the mathematical techniques for solving late-stage endgame problems that can stump top-ranking professionals. As a typical game of Go approaches its conclusion, the active regions of play become independent of one another, and the overall board position may be regarded as a sum of disconnected partial board positions. Combinatorial game theory, a branch of mathematics Berlekamp helped develop, has long been concerned with such sums of games. Here, it is applied to solving Go-related problems with a bewildering choice of similar-looking moves and subtle priority relationships. The theory presented in this book assigns each active area on the board an abstract value and then shows how to compare them to select the optimum move or add them up to determine the ideal outcome. Some of the values are familiar numbers or fractions, but most are more bizarre objects quite unlike anything in the existing Co literature. From these abstractions, the reader learns that positions seeming ro have the same numerical value can be crucially different while positions that appear completely different can be mathematically identical. A go player with an interest in mathematics or a mathematician interested in Go will not want to miss this book because it describes substantial connections between the two subjects which have been, until now, overlooked.

Mathematical Go Endgames: Nightmares for Professional Go Players

Humor & Entertainment

Wolfe, David

Puzzles & Games

Ishi Press

The ancient game of Go is one of the less obvious candidates for mathematical analysis. With the development of new concepts in combinatorial game theory, the authors have been able to analyze Go games and find solutions to real endgame problems that have stumped professional Go players. Go players with an interest in mathematics and mathematicians who work in game theory will not want to miss this book because it describes substantial connections between the two subjects that have been, until now, largely unrecognized.

Mathematical Go: Chilling Gets the Last Point

A K Peters/CRC Press

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