Self-Dual Codes and Invariant Theory

  • Gabriele Nebe
  • Eric M. Rains
  • Neil J.A. Sloane
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 17)

Table of contents

  1. Front Matter
    Pages I-XXVI
  2. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 1-28
  3. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 29-81
  4. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 83-102
  5. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 103-127
  6. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 129-170
  7. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 171-192
  8. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 193-226
  9. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 227-247
  10. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 249-284
  11. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 285-311
  12. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 313-345
  13. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 347-367
  14. Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
    Pages 369-390
  15. Back Matter
    Pages 391-430

About this book

Introduction

One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. In the past 35 years there have been hundreds of papers written about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.

It is also in part an encyclopedia that gives a very extensive list of the different types of self-dual codes and their properties, including tables of the best codes that are presently known. Besides self-dual codes, the book also discusses two closely-related subjects, lattices and modular forms, and quantum error-correcting codes.

This book, written by the leading experts in the subject, has no equivalent in the literature and will be of great interest to mathematicians, communication theorists, computer scientists and physicists.

Keywords

Code Error-correcting Code coding theory communication error-correcting codes invariant theory lattices modular forms optimal code quantum codes

Authors and affiliations

  • Gabriele Nebe
    • 1
  • Eric M. Rains
    • 2
  • Neil J.A. Sloane
    • 3
  1. 1.Lehrstuhl D für Mathematik Rheinisch-Westfälische Technische Hochschule AachenAachenGermany
  2. 2.Department of MathematicsUniversity of California at DavisDavisUSA
  3. 3.Internet and Network Systems Research AT&T Shannon LabsFlorham ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-30731-1
  • Copyright Information Springer 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-30729-7
  • Online ISBN 978-3-540-30731-0
  • Series Print ISSN 1431-1550
  • About this book