Lattices and Codes

A Course Partially Based on Lectures by Friedrich Hirzebruch

  • Wolfgang Ebeling

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

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Wolfgang Ebeling
    Pages 1-32
  3. Wolfgang Ebeling
    Pages 33-75
  4. Wolfgang Ebeling
    Pages 77-95
  5. Wolfgang Ebeling
    Pages 97-119
  6. Back Matter
    Pages 159-167

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 3rd edition, again numerous corrections and improvements have been made and the text has been updated.

Content
Lattices and Codes -Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes.

Readership
Graduate Students in Mathematics and Computer Science
Mathematicians and Computer Scientists

About the Author
Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany


Keywords

Leech lattice modular forms self-dual codes theta functions unimodular lattices weight enumerators

Authors and affiliations

  • Wolfgang Ebeling
    • 1
  1. 1.BurgdorfGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-658-00360-9
  • Copyright Information Springer Fachmedien Wiesbaden 2013
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-658-00359-3
  • Online ISBN 978-3-658-00360-9
  • Series Print ISSN 0932-7134
  • About this book