Algebraic Geometry Codes: Advanced Chapters (Mathematical Surveys and Monographs) - Hardcover

Michael Tsfasman; Serge Vladut; Dmitri Nogin

Hardcover

ISBN 10: 1470448653 ISBN 13: 9781470448653

Publisher: American Mathematical Society, 2019

Synopsis

Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to several domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes. The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.

About this title

About the Author

Michael Tsfasman: CNRS, Laboratoire de Mathématiques de Versailles, Versailles, France and Institute for Information Transmission Problems, Moscow, Russia and Independent University of Moscow, Moscow, Russia, Serge Vl du : Aix Marseille Université, Marseille, France and Institute for Information Transmission Problems, Moscow, Russia, Dmitry Nogin: Institute for Information Transmission Problems, Moscow, Russia

Edition details

• Publisher: American Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 1470448653
• ISBN 13: 9781470448653
• Binding: Hardcover
• Number of pages: 453