Volume: 238; 2019; 453 pp; Hardcover
MSC: Primary 14; 94; 11;
Print ISBN: 978-1-4704-4865-3
Product Code: SURV/238
List Price: $129.00
AMS Member Price: $103.20
MAA Member Price: $116.10
Electronic ISBN: 978-1-4704-5263-6
Product Code: SURV/238.E
List Price: $129.00
AMS Member Price: $103.20
MAA Member Price: $116.10
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Supplemental Materials
Algebraic Geometry Codes: Advanced Chapters
Share this pageMichael Tsfasman; Serge Vlǎduţ; Dmitry Nogin
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
Table of Contents
Algebraic Geometry Codes: Advanced Chapters
- Cover Cover11
- Title page i2
- Preface vii8
- Chapter 5. Curves with Many Points. I: Modular Curves 112
- Chapter 6. Class Field Theory 4960
- Chapter 7. Curves with Many Points. II 8798
- Chapter 8. Infinite Global Fields 141152
- Chapter 9. Decoding: Some Examples 195206
- Chapter 10. Sphere Packings 229240
- Chapter 11. Codes from Multidimensional Varieties 279290
- Chapter 12. Applications 335346
- Some Basic Facts from Volume 1 397408
- Bibliography 417428
- List of Names 437448
- Index 441452
- Back Cover Back Cover1466