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Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch de Wolfgang Ebeling

Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch: Advanced Lectures in Mathematics

Autor Wolfgang Ebeling
en Limba Engleză Paperback – 19 sep 2012
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.
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Specificații

ISBN-13: 9783658003593
ISBN-10: 3658003596
Pagini: 167
Ilustrații: XVI, 167 p. 50 illus.
Dimensiuni: 168 x 240 x 13 mm
Greutate: 0.32 kg
Ediția:3rd ed. 2013
Editura: Springer Fachmedien Wiesbaden
Colecția Springer Spektrum
Seria Advanced Lectures in Mathematics

Locul publicării:Wiesbaden, Germany

Public țintă

Graduate

Cuprins

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

Recenzii

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)

Notă biografică

Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany
Fields of research: Algebraic Geometry, Differential Topology, Singularities

Textul de pe ultima copertă

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


Caracteristici

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