# Introduction to the Theory of Error-Correcting Codes

John Wiley & Sons, Jul 2, 1998 - Mathematics - 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

### References from web pages

JSTOR: Introduction to the Theory of Error-Correcting Codes
Introduction to the theory of error-correcting codes (2nd edition), by Vera Pless. Pp 201. ?28-30. 1989. ISBN 0-471-61884-5 (Wiley) All natural languages ...

Feature Column from the AMS
Pless, V., Introduction to the Theory of Error-Correcting Codes, Wiley, New York, 1982. Pless, V. and W. Huffman, R.Brualdi (eds.),. ...
www.ams.org/ featurecolumn/ archive/ errors7.html

Existence of certain extremal self-dual codes - Information Theory ...
Pless, Introduction to the Theory of Error-Correcting Codes,. 2nd ed. F. J. macwilliams and. N. J. A. Sloane, The Theory. of. Error-. Correcting Codes. ...
ieeexplore.ieee.org/ iel1/ 18/ 3425/ 00119711.pdf

Math 810 Error-Correcting Codes
V. Pless, “Introduction to the theory of error-correcting codes,” 3rd edition,. Wiley, 1998. ISBN 0471190470. QA268 .P74 1992. O. Pretzel, “Error-correcting ...
www.mth.msu.edu/ ~jhall/ classes/ MTH810-07/ top2007.pdf

Joseph Malkevitch: Error Correcting Code Bibliography
Pless, V., Introduction to the Theory of Error-Correcting Codes, Wiley, New York, l982. Pretzel, O., Error-Correcting Codes and Finite Fields, Oxford Press, ...
york.cuny.edu/ ~malk/ biblio/ error-correct-codes-biblio.html

Error Correcting Codes
Pless, Vera, Introduction to the Theory of Error Correcting Codes. Welsh, Dominic, Codes and Cryptography. Proof of Shannon's theorem, among other things. ...
www.math.utah.edu/ ~carlson/ ugc/ ecc/

MATH 406/806
Vera Pless, Introduction to the Theory of Error-Correcting Codes (3rd edition), Wiley-Interscience, 1998. (A classic undergraduate text.) On course reserve. ...
www.mast.queensu.ca/ ~math406/

Michael E. O'Sullivan: Coding Theory
V. Pless, Introduction to the Theory of Error-Correcting Codes 3rd edition, Wiley-Interscience Series in Discrete Mathematics and Optimization, QA 268 P 55, ...
www-rohan.sdsu.edu/ ~mosulliv/ Courses/ ucoding04.html

Literatur zur Informations- und Codierungstheorie
Pless, V. Introduction to the theory of error-correcting codes, John Wiley, New York, 1989, 2. Aufl. Pötschke, D., ...
werner-heise.de/ lit_IC.html

Coding Theory
vs Pless, Introduction to the Theory of Error-Correcting Codes, Wiley, 1982, 1989;. QE 1302 Ple: another suitable text. 3. dg Hoffman et al., Coding Theory, ...
www.maths.sussex.ac.uk/ Staff/ JWPH/ TEACH/ CODING08/ sheet0.pdf