Codes on Algebraic Curves

Codes on Algebraic Curves by Serguei A. Stepanov.

This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of th...

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Bibliographic Details
Main Author: Stepanov, Serguei A. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer US : Imprint: Springer, 1999.
Edition:1st ed. 1999.
Series:Springer eBook Collection.
Subjects:
Algebra.
Electrical engineering.
Algebraic geometry.
Algorithms.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I. Error-Correcting Codes
  • 1 Codes and Their Parameters
  • 2 Bounds on Codes
  • 3 Examples and Constructions
  • II. Algebraic Curves and Varieties
  • 4 Algebraic Curves
  • 5 Curves over a Finite Field
  • 6 Counting Points on Curves over Finite Fields
  • III. Elliptic and Modular Curves
  • 7 Elliptic Curves
  • 8 Classical Modular Curves
  • 9 Reductions of Modular Curves
  • IV. Geometric Goppa Codes
  • 10 Constructions and Properties
  • 11 Examples
  • 12 Decoding Geometric Goppa Codes
  • 13 Bounds
  • List of Notations.

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