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© 2013

Lattices and Codes

A Course Partially Based on Lectures by Friedrich Hirzebruch

Textbook

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

  1. 1.BurgdorfGermany

About the authors

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

Fields of research: Algebraic Geometry, Differential Topology, Singularities

Bibliographic information

  • Book Title Lattices and Codes
  • Book Subtitle A Course Partially Based on Lectures by Friedrich Hirzebruch
  • Authors Wolfgang Ebeling
  • Series Title Advanced Lectures in Mathematics
  • 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 Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-658-00359-3
  • eBook ISBN 978-3-658-00360-9
  • Series ISSN 0932-7134
  • Edition Number 3
  • Number of Pages XVI, 167
  • Number of Illustrations 50 b/w illustrations, 0 illustrations in colour
  • Topics Mathematics, general
    Algebra
  • Buy this book on publisher's site
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Reviews

From the reviews of the third edition:

“In the book under review, Ebeling explores the mathematical theory of lattices and the ways that it is used by coding theorists. … I very much enjoyed reading Ebeling’s book. … This book contains some exciting mathematics, and I would recommend it to a graduate student or faculty member looking to learn about the field.” (Darren Glass, MAA Reviews, April, 2013)