Algebraic geometry codes

Algebraic geometry codes: advanced chapters

by Tsfasman, M. A., (Michael A.)

Type Book
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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…

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Title Statements

  • Full title :Algebraic geometry codes : advanced chapters / Michael Tsfasman, Serge Vladuts, Dmitry Nogin.

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 Alebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.

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Edition Statements

  • Publication Date:2019

Publication Statements

Notes

Algebraic-geometric codes / by M.A. Tsfasman, published: Dordrecht : Kluwer Academic Publishers, 1991. Republished as: Algebraic geometric codes : basic notions (Providence, R.I. : American Mathematical Society, 2007). Algebraic geometry codes : advanced chapters, continues 2007 publication, beginning at chapter 5.

The Physical Object

  • Description:1 online resource (x, 453 pages : : illustration

Edition Identifiers

  • ISBN:9781470452636, 1470452634
  • oclc:on1245833061
  • LC Classification:QA268
  • Dewey Decimal:003/.54

Subjects

Algebraic geometry -- Arithmetic proble… Algebraic geometry -- Curves Algebraic geometry -- Families, fibrati… Algebraic geometry -- Surfaces and high… Coding theory Géométrie algébrique Geometry, Algebraic Information and communication, circuits… Number theory Number theory -- Algebraic number theor… Number theory -- Finite fields and comm… Number theory -- Zeta and $L$-functions… Théorie des nombres

Writers

Tsfasman, M. A., (Michael A.) Nogin, Dmitry Vlăduț, S. G., (Serge G.)

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