Algebraic Geometric Codes: Basic Notions: 139 (Mathematical Surveys and Monographs) - Softcover

Michael Tsfasman (author)|Serge Vladut (author)|Dmitry Nogin (author)

Softcover

ISBN 10: 1470470071 ISBN 13: 9781470470074

Publisher: American Mathematical Society, 2007

Synopsis

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.

About this title

About the Author

Michael Tsfasman, French-Russian Poncelet Laboratory (CNRS and Ind. Univ. Moscow), Russia, Institut de Mathematiques de Luminy, France, and Institute for Information Transmission Problems, Moscow, Russia.

Serge Vladut, Institut de Mathematiques de Luminy, France, and Institute for Information Transmission Problems, Moscow, Russia.

Dmitry Nogin, Institute for Information Transmission Problems, Moscow, Russia.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2007
• Language: English
• ISBN 10: 1470470071
• ISBN 13: 9781470470074
• Binding: Paperback
• Number of pages: 338