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Cover: 9780192690678 | Error-Correcting Codes and Finite Fields | Oliver Pretzel | Buch
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Error-Correcting Codes and Finite Fields
Taschenbuch von Oliver Pretzel
Sprache: Englisch

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Beschreibung
This book provides engineers and computer scientists with all the tools necessary to implement modern error-processing techniques. It assumes only a basic knowledge of linear algebra and develops the mathematical theory in parallel with the codes. Central to the text are worked examples which motivate and explain the theory. The first part introduces the basic ideas of coding theory. The second and third cover the theory of finite fields and give a detailed treatment of BCH and Reed-Solomon codes. The fourth part is devoted to Goppa codes, both classical and geometric, concluding with the Skorobogatov-Vladut error processor. A special feature is a simplified (but rigorous) treatment of the geometry of curves.
This book provides engineers and computer scientists with all the tools necessary to implement modern error-processing techniques. It assumes only a basic knowledge of linear algebra and develops the mathematical theory in parallel with the codes. Central to the text are worked examples which motivate and explain the theory. The first part introduces the basic ideas of coding theory. The second and third cover the theory of finite fields and give a detailed treatment of BCH and Reed-Solomon codes. The fourth part is devoted to Goppa codes, both classical and geometric, concluding with the Skorobogatov-Vladut error processor. A special feature is a simplified (but rigorous) treatment of the geometry of curves.
Inhaltsverzeichnis
  • Part 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

  • Part 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

  • Part 3: BCH Codes and Other Polynomial Codes

  • 13: BCH codes as subcodes of Haming 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

  • Bibliography

  • Index

Details
Erscheinungsjahr: 1996
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780192690678
ISBN-10: 0192690671
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Pretzel, Oliver
Hersteller: OUP Oxford
Maße: 234 x 156 x 19 mm
Von/Mit: Oliver Pretzel
Erscheinungsdatum: 27.06.1996
Gewicht: 0,547 kg
Artikel-ID: 108634857
Inhaltsverzeichnis
  • Part 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

  • Part 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

  • Part 3: BCH Codes and Other Polynomial Codes

  • 13: BCH codes as subcodes of Haming 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

  • Bibliography

  • Index

Details
Erscheinungsjahr: 1996
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780192690678
ISBN-10: 0192690671
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Pretzel, Oliver
Hersteller: OUP Oxford
Maße: 234 x 156 x 19 mm
Von/Mit: Oliver Pretzel
Erscheinungsdatum: 27.06.1996
Gewicht: 0,547 kg
Artikel-ID: 108634857
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