Lattices and Codes

A Course Partially Based on Lectures by Friedrich Hirzebruch
3rd Auflage 2013
ISBN: 978-3-658-00359-3
Verlag: Springer

Buch, Englisch, 167 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 3183 g

Reihe: Advanced Lectures in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Ebeling, Wolfgang

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie

Inhaltsverzeichnis

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

Über Autor(innen)

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

Fields of research: Algebraic Geometry, Differential Topology, Singularities