Algebraic Geometry Codes: Advanced Chapters
About this Title
Michael Tsfasman, CNRS, Laboratoire de Mathématiques de Versailles, Versailles, France, Serge Vlǎduţ, Aix Marseille Université, Marseille, France and Dmitry Nogin, Institute for Information Transmission Problems, Moscow, Russia
Publication: Mathematical Surveys and Monographs
Publication Year: 2019; Volume 238
ISBNs: 978-1-4704-4865-3 (print); 978-1-4704-5263-6 (online)
MathSciNet review: 3966406
MSC: Primary 14G50; Secondary 11R37, 11R58, 11T71, 94-01, 94B27, 94B35
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.
Graduate students and researchers interested in algebraic geometry of curves and applications to coding theory.
Table of Contents
- Curves with many points. I: Modular curves
- Class field theory
- Curves with many points. II
- Infinite global fields
- Decoding: Some examples
- Sphere packings
- Codes from multidimensional varieties
- Appendix: Some basic facts from Volume 1