Title: Algebraic Geometric Codes: Basic Notions (Mathematical Surveys and Monographs, 139)
Publisher: American Mathematical Society
Publication Date: 2022
Language: English
ISBN 10: 1470470071
ISBN 13: 9781470470074
Binding: Soft cover
Condition: New

About this title

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 the Author

Michael Tsfasman, French-Russian Poncelet Laboratory (CNRS and Ind. Univ. Moscow), Russia, Institut de Math�matiques de Luminy, France, and Institute for Information Transmission Problems, Moscow, Russia, Serge Vlǎduţ, Institut de Math�matiques de Luminy, France, and Institute for Information Transmission Problems, Moscow, Russia, and Dmitry Nogin, Institute for Information Transmission Problems, Moscow, Russia

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