Introduction to the Theory of Error–Correcting Codes

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 Dist ributions.
Designs and Games.
Some Codes Are Unique.
Appendix.
References.
Index.

Nota biograficzna:
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.

Okładka tylna:
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.