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Algebraic Geometry Codes: Advanced Chapters
 
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 Vlǎduţ Aix Marseille Université, Marseille, France and Institute for Information Transmission Problems, Moscow, Russia
Dmitry Nogin Institute for Information Transmission Problems, Moscow, Russia
Algebraic Geometry Codes: Advanced Chapters
Hardcover ISBN:  978-1-4704-4865-3
Product Code:  SURV/238
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-5263-6
Product Code:  SURV/238.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-1-4704-4865-3
eBook: ISBN:  978-1-4704-5263-6
Product Code:  SURV/238.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Algebraic Geometry Codes: Advanced Chapters
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Algebraic Geometry Codes: Advanced Chapters
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 Vlǎduţ Aix Marseille Université, Marseille, France and Institute for Information Transmission Problems, Moscow, Russia
Dmitry Nogin Institute for Information Transmission Problems, Moscow, Russia
Hardcover ISBN:  978-1-4704-4865-3
Product Code:  SURV/238
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-5263-6
Product Code:  SURV/238.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-1-4704-4865-3
eBook ISBN:  978-1-4704-5263-6
Product Code:  SURV/238.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2382019; 453 pp
    MSC: Primary 14; 94; 11

    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.

    Readership

    Graduate students and researchers interested in algebraic geometry of curves and applications to coding theory.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2382019; 453 pp
MSC: Primary 14; 94; 11

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.

Readership

Graduate students and researchers interested in algebraic geometry of curves and applications to coding theory.

  • Chapters
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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