Algebraic geometry codes : advanced chapters
 Responsibility
 Michael Tsfasman, Serge Vlǎduţ, Dmitry Nogin.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2019]
 Copyright notice
 ©2019
 Physical description
 x, 453 pages : illustration ; 27 cm.
 Series
 Mathematical surveys and monographs no. 238.
Available online
At the library
Science Library (Li and Ma)
Stacks
Request (opens in new tab)
Call number  Status 

QA3 .A4 V.238  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Tsfasman, M. A. (Michael A.), 1954 author.
 Contributor
 Vlăduț, S. G. (Serge G.), 1954 author.
 Nogin, Dmitry, 1966 author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 417435) and index.
 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 Applications Appendix: Some basic facts from Volume 1 Bibliography List of names Index.
 (source: Nielsen Book Data)
 Summary

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 multidimensional 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Coding theory.
 Number theory.
 Geometry, Algebraic.
 Coding theory.
 Geometry, Algebraic.
 Number theory.
 Algebraic geometry > Curves > Curves.
 Information and communication, circuits > Theory of errorcorrecting codes and errordetecting codes > Theory of errorcorrecting codes and errordetecting codes.
 Algebraic geometry > Arithmetic problems. Diophantine geometry > Finite ground fields.
 Number theory > Algebraic number theory: global fields > Arithmetic theory of algebraic function fields.
 Number theory > Algebraic number theory: global fields > Algebraic numbers; rings of algebraic integers.
 Number theory > Finite fields and commutative rings (numbertheoretic aspects) > Algebraic coding theory; cryptography.
 Number theory > Zeta and $L$functions: analytic theory > Zeta and $L$functions in characteristic $p$.
 Number theory > Algebraic number theory: global fields > Class field theory.
 Number theory > Algebraic number theory: global fields > Zeta functions and $L$functions of number fields.
 Algebraic geometry > Families, fibrations > Fine and coarse moduli spaces.
 Algebraic geometry > Surfaces and higherdimensional varieties > Arithmetic ground fields.
Bibliographic information
 Publication date
 2019
 Copyright date
 2019
 Series
 Mathematical surveys and monographs ; volume 238
 Note
 "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."
 Related Work
 Algebraic geometry codes: basic notions.
 ISBN
 9781470448653 (hardcover alkaline paper)
 1470448653 (hardcover alkaline paper)