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

Pretzel, Oliver

Brossura

ISBN 10: 0192690671 ISBN 13: 9780192690678

Casa editrice: Oxford University Press, 2002

Riassunto

This textbook is a reprint of Chapters 1-20 of the original hardback edition. It provides the reader with the tools necessary to implement modern error-processing schemes. The material on algebraic geometry and geometric Goppa codes, which is not part of a standard introductory course on coding theory, has been omitted.

The book 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 cover the theory of finite fields and give a detailed treatment of BCH and Reed-Solomon codes. These parts are linked by their uses of Eulid's algorithm as a central technique. The fourth part treats classical Goppa codes.

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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

Dettagli dell?edizione

• Editore: Oxford University Press
• Data di pubblicazione: 2002
• ISBN 10: 0192690671
• ISBN 13: 9780192690678
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 360