Overview

This text provides an introduction to the theory of error-correcting codes and related topics in number theory, algebraic geometry and the theory of sphere packings. The material is presented in an easily understandable form. This book is devoted to geometric Goppa codes; the recently discovered areas which combines coding theory, algebraic geometry, number theory, and theory of sphere packings. It has an interdisciplinary nature and demonstrates the close interconnection of coding theory with various classical areas of mathematics. There are four main themes in the book, the first being a brief exposition of the basic concepts and facts of error-correcting code theory. The second is a complete presentation of the theory of algebraic curves; especially the curves defined over finite fields. The third is a detailed description of the theory of elliptic and modular codes, and their reductions modulo a prime number. The fourth is a construction of geometric Gappa codes producing rather long linear codes with very good parameters coming from algebraic curves, and with a lot of rational points.

Full Product Details

Author:   Serguei A. Stepanov
Publisher:   Springer Science+Business Media
Imprint:   Kluwer Academic/Plenum Publishers
Edition:   1999 ed.
Dimensions:   Width: 15.20cm , Height: 2.50cm , Length: 22.90cm
Weight:   1.580kg
ISBN:  

9780306461446

ISBN 10:   0306461447
Pages:   350
Publication Date:   31 July 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions