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.
Spis treści
Introductory Concepts.
Useful Background.
A Double-Error-Correcting BCH Code and a Finite Field of 16 Elements.
Finite Fields.
Cyclic Codes.
Group of a Code and Quadratic Residue (QR) Codes.
Bose-Chaudhuri-Hocquenghem (BCH) Codes.
Weight Distributions.
Designs and Games.
Some Codes Are Unique.
Appendix.
References.
Index.
O autorze
VERA PLESS is Professor of Mathematics and Computer Science and a University Scholar at the University of Illinois at Chicago. Professor Pless holds a Ph D in mathematics from Northwestern University.
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