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Springer Spektrum - Mathematik | Lattices and Codes - A Course Partially Based on Lectures by Friedrich Hirzebruch

Lattices and Codes

A Course Partially Based on Lectures by Friedrich Hirzebruch

Ebeling, Wolfgang

3rd ed. 2013, XVI, 167 p. 50 illus.

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  • Master course on the relationship between coding theory and the 
  • theory of integral lattices

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


Content Level » Graduate

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

Related subjects » Algebra - Mathematik

Table of contents 

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

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