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

ISBN-13: 9783658003593 / Angielski / Miękka / 2012 / 167 str.

Wolfgang Ebeling

Opis

The purpose of coding theory is the design of efficient systems forthe transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisinglyproblems which are interesting for the design of codes turn out to beclosely related to problems studied partly earlier and independentlyin pure mathematics. In this book, examples of such connections arepresented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book providesat the same time an introduction to the theory of integral latticesand modular forms and to coding theory.
In the 3rd edition, again numerous corrections and improvements havebeen made and the text has been updated."

Recenzje

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)

Spis treści

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

O autorze

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

Fields of research: Algebraic Geometry, Differential Topology, Singularities

Blurb

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