Introduction to coding theory Juergen Bierbrauer.
Material type: TextSeries: Discrete mathematics and its applicationsPublication details: Boca Raton : Chapman & Hall/CRC, c2005.Description: xxiii, 390 p. : ill. ; 24 cmISBN:- 9781584884217
- 003.54 23 B588
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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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