Lattices and Codes

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

   PDF

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.

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

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)

• Burgdorf, Germany

  Wolfgang Ebeling

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

Fields of research: Algebraic Geometry, Differential Topology, Singularities

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