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Self-dual codes and invariant theory
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 thi...
| Auteurs principaux : | , , |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Self-dual codes and invariant theory / Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane |
| Publié : |
Berlin, Heidelberg :
Springer Berlin Heidelberg
, 2006 Springer e-books |
| Collection : | Algorithms and computation in mathematics ; 17 |
| Titre de l'ensemble : | Algorithms and computation in mathematics vol. 17 |
| Disponibilité : | L'accès complet au document est réservé aux usagers des établissements qui en ont fait l'acquisition |
| Contenu : | The Type of a Self-Dual Code. Weight Enumerators and Important Types. Closed Codes. The Category Quad. The Main Theorems. Real and Complex Clifford Groups. Classical Self-Dual Codes. Further Examples of Self-Dual Codes. Lattices. Maximal Isotropic Codes and Lattices. Extremal and Optimal Codes. Enumeration of Self-Dual Codes. Quantum Codes |
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| Documents associés : | Autre format:
Self-dual codes and invariant theory |
| Résumé : | 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 |
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| Notes : | L'impression du document génère 456 p. Description d'après consultation du 22 avril 2011 Titre provenant de la page de titre du document numérisé |
| Historique des publications : | Numérisation de l'édition de Berlin : Springer, 2006 |
| Configuration requise : | Nécessite un lecteur de fichier PDF |
| Bibliographie : | Bibliogr. p. [391]-415. Index |
| ISBN : | 978-3-540-30731-0 |
| Type de ressource électronique : | Fichiers PDF |