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9781402012037

Coding Theory and Number Theory

by ;
  • ISBN13:

    9781402012037

  • ISBN10:

    1402012039

  • Format: Hardcover
  • Copyright: 2003-04-01
  • Publisher: Kluwer Academic Pub
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Summary

This introductory book, which grew out of lectures given at the Mathematics Institute of Würzburg University, proposes a combination of coding theory and number theory. Chapter 1 gives a standard course of linear codes. The next two chapters treat a link between coding theory and number theory. Chapter 4 is a systematic study of algebraic-geometric codes and in Chapter 5 a connection between binary linear codes and theta functions is discussed. The book is designed to teach undergraduates and graduates the basic ideas and techniques of coding theory and number theory.

Table of Contents

Preface
Linear Codesp. 1
Diophantine Equations and Cyclic Codesp. 17
Elliptic Curves, Hecke Operators and Weight Distribution of Codesp. 23
Algebraic-Geometric Codes and Modular Curve Codesp. 49
Theta Functions and Self-Dual Codesp. 77
The Kloosterman Codes and Distribution of the Weightsp. 117
Referencesp. 141
Indexp. 145
Table of Contents provided by Blackwell. All Rights Reserved.

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