Self-Dual Codes and Invariant Theory: 17 - Brossura

Nebe, Gabriele; Rains, Eric M.; Sloane, Neil J. A.

Brossura

ISBN 10: 3642068014 ISBN 13: 9783642068010

Casa editrice: Springer, 2010

Riassunto

One of the most remarkable theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. This book develops a new theory which is powerful enough to include all the earlier generalizations. It is also in part an extensive encyclopedia listing the different types of self-dual codes and their properties.

Su questo libro

Recensione

From the reviews:

"This book under review the general notions of form rings and their representations ... . This book, introducing a new unifying theory and its applications to a wealth of substantial examples, is certainly written for experts in the field." (Jürgen Müller, Mathematical Reviews, Issue 2007 d)

Dalla quarta di copertina

One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. In the past 35 years there have been hundreds of papers written about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.

It is also in part an encyclopedia that gives a very extensive list of the different types of self-dual codes and their properties, including tables of the best codes that are presently known. Besides self-dual codes, the book also discusses two closely-related subjects, lattices and modular forms, and quantum error-correcting codes.

This book, written by the leading experts in the subject, has no equivalent in the literature and will be of great interest to mathematicians, communication theorists, computer scientists and physicists.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2010
• ISBN 10: 3642068014
• ISBN 13: 9783642068010
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 460