Hardcover ISBN:  9781470448653 
Product Code:  SURV/238 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
Electronic ISBN:  9781470452636 
Product Code:  SURV/238.E 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 

Book DetailsMathematical Surveys and MonographsVolume: 238; 2019; 453 ppMSC: 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 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.ReadershipGraduate 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


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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 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.
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