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.
Rezensionen / Stimmen
'... the text is clear and well-written with many helpful examples... this book should prove useful to students trying to learn about geometric codes.' * Zentralblatt fuer Mathematik, 884 *
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 242 mm
Breite: 164 mm
Dicke: 17 mm
Gewicht
ISBN-13
978-0-19-850039-1 (9780198500391)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Senior Lecturer in MathematicsSenior Lecturer in Mathematics, Imperial College
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
