Error-Correcting Linear Codes

Classification by Isometry and Applications

  • Anton Betten
  • Michael Braun
  • Harald Fripertinger
  • Adalbert Kerber
  • Axel Kohnert
  • Alfred Wassermann

Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 18)

Table of contents

  1. Front Matter
    Pages I-XXIX
  2. Pages 1-77
  3. Pages 137-210
  4. Pages 211-366
  5. Pages 661-752
  6. Back Matter
    Pages 753-798

About this book

Introduction

This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players.
The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes. Up until now, these advanced topics have only been covered in research papers.
The present book provides access to these results at a level which is suitable for graduate students of mathematics, computer science and engineering as well as for researchers.

Keywords

Algebra Computer algorithms coding theory computer science error-correcting codes finite field linear codes

Authors and affiliations

  • Anton Betten
    • 1
  • Michael Braun
    • 2
  • Harald Fripertinger
    • 3
  • Adalbert Kerber
    • 4
  • Axel Kohnert
    • 4
  • Alfred Wassermann
    • 4
  1. 1.Department of MathematicsColorado State UniversityFort CollinsUSA
  2. 2.Siemens CT IC 3MünchenGermany
  3. 3.Institut für MathematikKarl-Franzens-Universität GrazGrazAustria
  4. 4.Mathematisches InstitutUniversität BayreuthBayreuthGermany

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-31703-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-28371-3
  • Online ISBN 978-3-540-31703-6
  • Series Print ISSN 1431-1550
  • About this book
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