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Introduction to coding theory Juergen Bierbrauer.

By: Material type: TextTextSeries: Discrete mathematics and its applicationsPublication details: Boca Raton : Chapman & Hall/CRC, c2005.Description: xxiii, 390 p. : ill. ; 24 cmISBN:
  • 9781584884217
Subject(s): DDC classification:
  • 003.54 23 B588
Contents:
I. An elementary introduction to coding -- 1. The concept of coding -- 2. Binary linear codes -- 3. General linear codes -- 4. Singleton bound and Reed-Solomon codes -- 5. Recursive constructions I -- 6. Universal hashing -- 7. Designs and the binary Golay code -- 8. Shannon entropy -- 9. Asymptotic results -- 10. 3-dimensional codes, projective planes -- 11. Summary and outlook -- II. Theory and applications of codes -- 12. Subfield codes and trace codes -- 13. Cyclic codes -- 14. Recursive constructions, covering radius -- 15. OA in statistics and computer science -- 16. The geometric description of codes -- 17. Additive codes -- 18. The last chapter-- References-- Index.
Summary: Although its roots lie in information theory, the applications of coding theory extend to statistics, cryptography, and many areas of mathematics. This book introduces the theory of error-correcting codes and its application. It presents an approach that includes sections devoted to basic concepts such as congruences and fields of prime order.
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Includes bibliographical references ( p. 371-382 ) and index.

I. An elementary introduction to coding --
1. The concept of coding --
2. Binary linear codes --
3. General linear codes --
4. Singleton bound and Reed-Solomon codes --
5. Recursive constructions I --
6. Universal hashing --
7. Designs and the binary Golay code --
8. Shannon entropy --
9. Asymptotic results --
10. 3-dimensional codes, projective planes --
11. Summary and outlook --

II. Theory and applications of codes --
12. Subfield codes and trace codes --
13. Cyclic codes --
14. Recursive constructions, covering radius --
15. OA in statistics and computer science --
16. The geometric description of codes --
17. Additive codes --
18. The last chapter--

References--
Index.

Although its roots lie in information theory, the applications of coding theory extend to statistics, cryptography, and many areas of mathematics. This book introduces the theory of error-correcting codes and its application. It presents an approach that includes sections devoted to basic concepts such as congruences and fields of prime order.

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