Advanced Lectures in Mathematics

Lattices and Codes

A Course Partially Based on Lectures by F. Hirzebruch

Authors: Ebeling, Wolfgang

  • Modern Aspects in the Design of Codes

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  • ISBN 978-3-322-90014-2
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About this Textbook

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.

About the authors

Prof. Dr. Wolfgang Ebeling, Department of Mathematics, Universit├Ąt Hannover, Germany.

Table of contents (5 chapters)

  • Lattices and Codes

    Ebeling, Wolfgang

    Pages 1-37

  • Theta Functions and Weight Enumerators

    Ebeling, Wolfgang

    Pages 39-86

  • Even Unimodular Lattices

    Ebeling, Wolfgang

    Pages 87-108

  • The Leech Lattice

    Ebeling, Wolfgang

    Pages 109-134

  • Lattices over Integers of Number Fields and Self-Dual Codes

    Ebeling, Wolfgang

    Pages 135-174

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-322-90014-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Lattices and Codes
Book Subtitle
A Course Partially Based on Lectures by F. Hirzebruch
Authors
Series Title
Advanced Lectures in Mathematics
Copyright
2002
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
eBook ISBN
978-3-322-90014-2
DOI
10.1007/978-3-322-90014-2
Series ISSN
0932-7134
Edition Number
2
Number of Pages
XVIII, 188
Topics