Codes and Algebraic Curves

by Oliver Pretzel

Overview

A fascinating branch of mathematics since antiquity, the geometry of curves has been extensively developed and 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 expanded and updated version of one part of the author's successful book Error-Correcting Codes and Finite Fields. Here he gives an elementary introduction to Goppa codes and includes many examples, calculations, and applications. The first part of the book emphasizes motivations, giving precedence to applications over proofs. The second part then provides the formal theory, with some concepts and proofs simplified without sacrificing rigor.

Product Details

ISBN-13:	9780198500391
Publisher:	Oxford University Press
Publication date:	03/05/1998
Series:	Oxford Lecture Series in Mathematics and Its Applications , #8
Edition description:	New Edition
Pages:	208
Product dimensions:	9.52(w) x 6.46(h) x 0.67(d)

About the Author

Imperial College, London

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