Lattices and Codes
A Course Partially Based on Lectures by Friedrich Hirzebruch
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Beschreibung
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
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.
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
Autor*in
Wolfgang Ebeling
Themen in »Lattices and Codes«
Leech lattice modular forms self-dual codes theta functions unimodular lattices weight enumerators
Stimmen zu »Lattices and Codes«
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)
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