Algebraic Geometric Codes: Basic Notions: Basic Notions
Michael A. Tsfasman · Serge G. Vlăduț · Dmitry Nogin
Jan 2007 · Mathematical Surveys and Monographs Book 139 · American Mathematical Soc.
Ebook
338
Pages
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About this ebook
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 almostalways 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 anintroduction 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.
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