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.
At the library
Science Library (Li and Ma)
Stacks
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| Call number | Status |
|---|---|
| QA3 .A4 V.238 |
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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 417-435) 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 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.
(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 error-correcting codes and error-detecting codes > Theory of error-correcting codes and error-detecting 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 (number-theoretic 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 higher-dimensional 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)
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