Error-Correcting Codes and Finite Fields. Student Edition (Oxford Applied Mathematics and Computing Science Series)

Pretzel, Oliver

ISBN 10: 0192690671 / ISBN 13: 9780192690678

Editore: Oxford University Press, 1996

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Dati bibliografici

• Titolo: Error-Correcting Codes and Finite Fields. Student Edition (Oxford Applied Mathematics and Computing Science Series)
• Editore: Oxford University Press
• Data di pubblicazione: 1996
• Lingua: Inglese
• ISBN 10: 0192690671
• ISBN 13: 9780192690678
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

This book provides the reader with all the tools necessary to implement modern error-processing schemes. 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 book is in four parts. The first introduces the basic ideas of coding theory. The second and third parts cover the theory of finite fields and give a detailed treatment of BCH and Reed-Solomon codes. These parts are linked by their use of Euclid's algorithm as a central technique. The fourth part is devoted to Goppa codes, both classical and geometric, concluding with the Skorobogatov-Vladut error processor. A special feature of this part is a simplified (but rigorous) treatment of the geometry of curves.

Contenuti

• 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