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Lattices and Codes

A Course Partially Based on Lectures by Friedrich Hirzebruch

  • Textbook
  • © 2013

Overview

Authors:
  1. Wolfgang Ebeling

    1. Burgdorf, Germany

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  • Master course on the relationship between coding theory and the
  • theory of integral lattices
  • Linking classical mathematics to modern aspects in the design of codes
  • With many examples and connections to number theory and geometry

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Lattices and Codes

    • Wolfgang Ebeling
    Pages 1-32

  3. Theta Functions and Weight Enumerators

    • Wolfgang Ebeling
    Pages 33-75

  4. Even Unimodular Lattices

    • Wolfgang Ebeling
    Pages 77-95

  5. The Leech Lattice

    • Wolfgang Ebeling
    Pages 97-119

  6. Lattices over Integers of Number Fields and Self-Dual Codes

    • Wolfgang Ebeling
    Pages 121-157

  7. Back Matter

    Pages 159-167
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Burgdorf, Germany

    Wolfgang Ebeling

About the author

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

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Fachmedien Wiesbaden 2013

  • Softcover ISBN: 978-3-658-00359-3Published: 19 September 2012

  • eBook ISBN: 978-3-658-00360-9Published: 18 September 2012

  • Series ISSN: 0932-7134

  • Series E-ISSN: 2512-7039

  • Edition Number: 3

  • Number of Pages: XVI, 167

  • Number of Illustrations: 50 b/w illustrations

  • Topics: Mathematics, general, Algebra

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