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Codes and Algebraic Curves : Oxford Lecture Series in Mathematics and Its Applications - Oliver Pretzel

Codes and Algebraic Curves

Oxford Lecture Series in Mathematics and Its Applications

Hardcover Published: 1st December 1997
ISBN: 9780198500391
Number Of Pages: 208

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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 an updated 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, and applications 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.

Industry Reviews

The text is written in an approachable style. ' 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

Part 1: Codes from algebraic curves 1: Introduction: curves and codes 2: Algebraic curves 3: Functions on algebraic curves 4: A survey of the theory of algebraic curves 5: Geometric Goppa codes 6: Basic error processing 7: Full error processing Part 2: Fields of algebraic functions 8: Introduction: the algebraic approach 9: Function fields and places 10: Valuations 11: Divisors 12: Repartitions and differentials 13: Extensions of function fields 14: Curves and function fields 15: More on Goppa codes

ISBN: 9780198500391
ISBN-10: 0198500394
Series: Oxford Lecture Series in Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 208
Published: 1st December 1997
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.2 x 16.0  x 1.6
Weight (kg): 0.44