Codes and Algebraic Curves

Zusatztext '... the text is clear and well-written with many helpful examples... this book should prove useful to students trying to learn about geometric codes.' Klappentext 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. Zusammenfassung This is an updated and extended version of the last part of Dr Pretzel's successful book Error Correcting Codes and Finite Fields. It provides an introduction to the geometry of curves over finite fields. and uses the theory for a detailed investigation of geometric Goppa codes, a new and important area of coding theory. Inhaltsverzeichnis 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

Product details

• Authors: Oliver Pretzel, Oliver (Senior Lecturer in Mathematics Pretzel, Pretzel Oliver
• Publisher: Oxford University Press
• Languages: English
• Product format: Hardback
• Released: 08.01.1998
• EAN: 9780198500391
• ISBN: 978-0-19-850039-1
• No. of pages: 208
• Series: Oxford Lecture Series in Mathematics and Its Applications; Oxford Lecture Series in Mathe; Oxford Lecture Series in Mathematics and Its Applications; Oxford Lecture Mathematics and
• Subjects: Guides; Natural sciences, medicine, IT, technology > Mathematics > Geometry; Social sciences, law, business > Media, communication > Book trade, library system; COMPUTERS / Information Theory, MATHEMATICS / Applied, MATHEMATICS / Geometry / Algebraic, Algebraic Geometry, Information theory, Maths for scientists, Maths for engineers