Codes and Algebraic Curves

Hardcover | January 1, 1998

byOliver Pretzel

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The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is anupdated and extended version of the last part of the successful book Error-Correcting Codes and Finite Fields. It provides an elementary introduction to Goppa codes, and includes many examples, calculations, and applications. The book is in two parts with an emphasis on motivation, andapplications of the theory take precedence over proofs of theorems. The formal theory is, however, provided in the second part of the book, and several of the concepts and proofs have been simplified without sacrificing rigour.

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The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is anupdated and extended version of the last part of...

Oliver Pretzel is at Imperial College.

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Format:HardcoverDimensions:208 pages, 9.21 × 6.14 × 0.63 inPublished:January 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198500394

ISBN - 13:9780198500391

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Table of Contents

Part 1: Codes from algebraic curves1. Introduction: curves and codes2. Algebraic curves3. Functions on algebraic curves4. A survey of the theory of algebraic curves5. Geometric Goppa codes6. Basic error processing7. Full error processingPart 2: Fields of algebraic functions8. Introduction: the algebraic approach9. Function fields and places10. Valuations11. Divisors12. Repartitions and differentials13. Extensions of function fields14. Curves and function fields15. More on Goppa codes

Editorial Reviews

' So, to learn enough algebraic geometry to understand Goppa's codes, a student could take this book and study it with advantage...gives any student an excellent start' Bulletin London Mathematical Society