# Introduction to the Theory of Error-Correcting Codes

John Wiley & Sons, Jul 2, 1998 - Computers - 207 pages
A complete introduction to the many mathematical tools used to solve practical problems in coding.

Mathematicians have been fascinated with the theory of error-correcting codes since the publication of Shannon's classic papers fifty years ago. With the proliferation of communications systems, computers, and digital audio devices that employ error-correcting codes, the theory has taken on practical importance in the solution of coding problems. This solution process requires the use of a wide variety of mathematical tools and an understanding of how to find mathematical techniques to solve applied problems.

Introduction to the Theory of Error-Correcting Codes, Third Edition demonstrates this process and prepares students to cope with coding problems. Like its predecessor, which was awarded a three-star rating by the Mathematical Association of America, this updated and expanded edition gives readers a firm grasp of the timeless fundamentals of coding as well as the latest theoretical advances. This new edition features:
* A greater emphasis on nonlinear binary codes
* An exciting new discussion on the relationship between codes and combinatorial games
* Updated and expanded sections on the Vashamov-Gilbert bound, van Lint-Wilson bound, BCH codes, and Reed-Muller codes
* Expanded and updated problem sets.

Introduction to the Theory of Error-Correcting Codes, Third Edition is the ideal textbook for senior-undergraduate and first-year graduate courses on error-correcting codes in mathematics, computer science, and electrical engineering.

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### Contents

 Useful Background 17 J H Conway and N J A Sloane Sphere Packings Lattices and Groups 33 A DoubleErrorCorrecting BCH Code and a Finite Field 39 R A Brualdi and V Pless Greedy codes JCT A64 1993 1030 46 Problems 48 Cyclic Codes 67 Group of a Code and Quadratic Residue QR Codes 85 BoseChaudhuriHocquenghem BCH Codes 109
 Weight Distributions 123 Designs and Games 143 Some Codes Are Unique 169 Appendix 189 References 199 and P Sole The Z4linearity of Kerdock Preparata Goethals 202 Copyright

### About the author (1998)

VERA PLESS is Professor of Mathematics and Computer Science and a University Scholar at the University of Illinois at Chicago. Professor Pless holds a PhD in mathematics from Northwestern University.