**Mathematical Surveys and Monographs**

Volume: 139;
2007;
338 pp;
Hardcover

MSC: Primary 14; 94; 11;

Print ISBN: 978-0-8218-4306-2

Product Code: SURV/139

List Price: $97.00

Individual Member Price: $77.60

**Electronic ISBN: 978-1-4704-1366-8
Product Code: SURV/139.E**

List Price: $97.00

Individual Member Price: $77.60

#### Supplemental Materials

# Algebraic Geometric Codes: Basic Notions

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*Michael Tsfasman; Serge Vlǎduţ; Dmitry Nogin*

The book is devoted to the theory of algebraic geometric codes, a subject
formed on the border of several domains of mathematics. On one side there
are such classical areas as algebraic geometry and number theory; on the
other, information transmission theory, combinatorics, finite geometries,
dense packings, etc.

The authors give a unique perspective on the subject. Whereas most books
on coding theory build up coding theory from within, starting from
elementary concepts and almost always finishing without reaching a certain
depth, this book constantly looks for interpretations that connect coding
theory to algebraic geometry and number theory.

There are no prerequisites other than a standard algebra graduate course.
The first two chapters of the book can serve as an introduction to coding
theory and algebraic geometry respectively. Special attention is given to
the geometry of curves over finite fields in the third chapter. Finally,
in the last chapter the authors explain relations between all of these:
the theory of algebraic geometric codes.

#### Table of Contents

# Table of Contents

## Algebraic Geometric Codes: Basic Notions

- Contents v6 free
- Preface ix10 free
- Advice to the Reader xvii18 free
- Chapter 1. Codes 122 free
- Chapter 2. Curves 6990
- Chapter 3. Curves over Finite Fields 133154
- Chapter 4. Algebraic Geometry Codes 191212
- Appendix. Summary of Results and Tables 287308
- Bibliography 309330
- List of Names 329350
- Index 331352

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and coding theory.

#### Reviews

...the authors have done a great service to the mathematical community. Written in an utmost lucid and thorough style, this book on a rapidly growing new area of contemporary, interdisciplinary mathematics, together with its forthcoming companion volume “Advanced Chapters”, must be seen as the most profound and topical exposition of its kind. It is of nearly universal utility for both specialists and non-specialists in the field, and it is very likely to become the unrivalled standard text in the related literature. We share the authors' hope that this monograph will have a propelling impact, and that it will be of some use for those who intend to choose algebraic geometric coding theory as their own area of research in the future.

-- Zentralblatt MATH

The book under review successfully introduces the necessary background needed for the study of AG codes. ...it will be a standard reference for beginners as well as for active researchers in this beautiful subject.

-- Mathematical Reviews