Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics)

Betten, Anton, Braun, Michael, Fripertinger, Harald, Kerber,

ISBN 10: 3540283714 / ISBN 13: 9783540283713

Verlag: Springer, 2006

Beschreibung

Like New.

Bestandsnummer des Verkäufers ERICA75835402837145

Bibliografische Details

• Titel: Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics)
• Verlag: Springer
• Erscheinungsjahr: 2006
• Sprache: Englisch
• ISBN-10: 3540283714
• ISBN-13: 9783540283713
• Einband: Hardcover
• Zustand: Like New
• Buchtyp: book

Über diesen Titel

Inhaltsangabe

This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.

Von der hinteren Coverseite

This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players.
The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes. Up until now, these advanced topics have only been covered in research papers.
The present book provides access to these results at a level which is suitable for graduate students of mathematics, computer science and engineering as well as for researchers.