Introduction to the Theory of Error-Correcting Codes

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John Wiley & Sons, Jul 2, 1998 - Computers - 207 pages
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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
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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.