Algebraic Geometric Codes: Basic Notions
Seiten
2007
American Mathematical Society (Verlag)
978-1-4704-7007-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-7007-4 (ISBN)
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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.
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.
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.
Codes
Curves
Curves over finite fields
Algebraic geometry codes
Summary of results and tables
Bibliography
List of names
Index
| Erscheinungsdatum | 08.07.2025 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-7007-1 / 1470470071 |
| ISBN-13 | 978-1-4704-7007-4 / 9781470470074 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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