Lattices and Codes

A Course Partially Based on Lectures by F. Hirzebruch

  • Wolfgang Ebeling
Part of the Advanced Lectures in Mathematics book series (ALM)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Wolfgang Ebeling
    Pages 1-37
  3. Wolfgang Ebeling
    Pages 39-86
  4. Wolfgang Ebeling
    Pages 87-108
  5. Wolfgang Ebeling
    Pages 109-134
  6. Back Matter
    Pages 175-190

About this book

Introduction

The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory.
In the 2nd edition numerous corrections have been made. More basic material has been included to make the text even more self-contained. A new section on the automorphism group of the Leech lattice has been added. Some hints to new results have been incorporated. Finally, several new exercises have been added.

Keywords

Codierungstheorie Even Unimodular Lattices Leech Lattice Number theory algebra coding theory

Authors and affiliations

  • Wolfgang Ebeling
    • 1
  1. 1.Institut für MathematikUniversität HannoverHannoverGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-90014-2
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2002
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-528-16497-3
  • Online ISBN 978-3-322-90014-2
  • Series Print ISSN 0932-7134
  • About this book