Self-Dual Codes and Invariant Theory

Gabriele Nebe

ISBN 10: 354030729X / ISBN 13: 9783540307297

Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Feb 2006, 2006

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Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 460 pp. Englisch.

Codice articolo 9783540307297

Dati bibliografici

• Titolo: Self-Dual Codes and Invariant Theory
• Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Feb 2006
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 354030729X
• ISBN 13: 9783540307297
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 246 L x 175 A x 31 P (millimetri) 246 millimetri di larghezza per 175 millimetri di altezza per 31 millimetri di profondità
• Peso: 953 grammi

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Riassunto

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.