Error-Correcting Codes and Finite Fields by Oliver PretzelError-Correcting Codes and Finite Fields by Oliver Pretzel

Error-Correcting Codes and Finite Fields

byOliver Pretzel

Paperback | April 30, 1999

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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 oncoding 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 parttreats classical Goppa codes.
O. L. R. Pretzel is at Imperial College of Science and Technology, London.
Title:Error-Correcting Codes and Finite FieldsFormat:PaperbackDimensions:356 pages, 9.21 × 6.14 × 0.75 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0192690671

ISBN - 13:9780192690678

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Table of Contents

Part 1: Basic Coding Theory1. Introduction2. Block codes, weight, and distance3. Linear codes4. Error processing for linear codes5. Hamming codes and the binary Golay codesAppendix LA Linear algebraPart 2: Finite Fields6. Introduction and an example7. Euclid's algorithm8. Invertible and irreducible elements9. The construction of fields10. The structure of finite fields11. Roots of polynomials12. Primitive elementsAppendix PF Polynomials over a FieldPart 3: BCH Codes and Other Polynomial Codes13. BCH codes as subcodes of Haming codes14. BCH codes as polynomial codes15. BCH error correction: (1) the fundamental equation16. BCH error correction (2) an algorithm17. Reed-Solomon codes and burst error correction18. Bounds on codesBibliographyIndex

Editorial Reviews

"Covers the standard course in the theory of finite fields and error-correcting codes, and contains a comprehensive introduction to algebraic-geometric codes." --Mathematical Reviews