Error-correcting codes and finite fields

Error-correcting codes and finite fields

by Pretzel, Oliver

Type Book
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Starting with the elementary ideas of parity check codes, this work takes the reader via BCH and Reed-Solomon codes all the way to the geometric Goppa codes. The necessary mathematics is developed in parallel with the applications.

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Title Statements

  • Full title :Error-correcting codes and finite fields / Oliver Pretzel.

Summary

Starting with the elementary ideas of parity check codes, this work takes the reader via BCH and Reed-Solomon codes all the way to the geometric Goppa codes. The necessary mathematics is developed in parallel with the applications.

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Edition Statements

  • Publication Date:1992.

Publication Statements

The Physical Object

  • Description:xiii, 398 pages : : illustrations ; : 24 cm.

Edition Identifiers

  • ISBN:0198596782, 9780198596783
  • oclc:ocm25282642
  • LC Classification:QA268
  • Dewey Decimal:003/.54

Table of Contents

Pt. 1. Basic Coding Theory. 1. Introduction. 2. Block codes, weight, and distance. 3. Linear codes. 4. Error processing for linear codes. 5. Hamming codes and the binary Golay codes -- Appendix LA: Linear algebra -- Pt. 2. Finite Fields. 6. Introduction and an example. 7. Euclid's algorithm. 8. Invertible and irreducible elements. 9. The construction of fields. 10. The structure of finite fields. 11. Roots of polynomials. 12. Primitive elements -- Appendix PF: Polynomials over a field -- Pt. 3. BCH Codes and Other Polynomial Codes. 13. BCH codes as subcodes of Hamming codes. 14. BCH codes as polynomial codes. 15. BCH error correction: (1) the fundamental equation. 16. BCH error correction: (2) an algorithm. 17. Reed-Solomon codes and burst error correction. 18. Bounds on codes -- Pt. 4. Classical and Geometric Goppa Codes. 19. Classical Goppa codes. 20. Classical Goppa codes: error processing. 21. Introduction to algebraic curves. 22. Functions on algebraic curves. 23. A survey of the theory of algebraic curves. 24. Geometric Goppa codes. 25. An error processor for geometric Goppa codes.

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Subjects

Algèbre linéaire Aufsatzsammlung Codage (théorie du) Codes correcteurs d'erreurs (Théorie de… Error-correcting codes (Information the… Fehlerkorrekturcode Finite fields (Algebra) Information

Writers

Pretzel, Oliver

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