Algebraic Geometric Codes: Basic Notions
About this Title
Michael Tsfasman, French-Russian Poncelet Laboratory (CNRS and Ind. Univ. Moscow), Moscow, Russia, Serge Vlǎduţ, Institut de Mathématiques de Luminy, Luminy, France and Dmitry Nogin, Institute for Information Transmission Problems, Moscow, Russia
Publication: Mathematical Surveys and Monographs
Publication Year 2007: Volume 139
ISBNs: 978-0-8218-4306-2 (print); 978-1-4704-1366-8 (online)
MathSciNet review: MR2339649
MSC: Primary 94B27; Secondary 11R58, 11T71, 14G50, 94-01
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.
Graduate students and research mathematicians interested in algebraic geometry and coding theory.
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