Nebe, G. and Rains, E. M. and Sloane, N. J. A. (2004) Codes and invariant theory. Mathematische Nachrichten, 274-275 (1). pp. 104-116. ISSN 0025-584X. doi:10.1002/mana.200310204. https://resolver.caltech.edu/CaltechAUTHORS:20171004-091341996
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Abstract
The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and modules. The proof of the theorem uses a categorical approach, and will be the subject of a forthcoming book. However, the theorem can be stated and applied without using category theory, and we illustrate it here by applying it to generalized doubly-even codes over fields of characteristic 2, doubly-even codes over ℤ/2fℤ, and self-dual codes over the noncommutative ring F_q + F_qu, where u^2 = 0.
Item Type: | Article | ||||||||||||
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Additional Information: | © 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. Issue online: 9 September 2004; Version of record online: 9 September 2004; Manuscript Accepted: 24 February 2004; Manuscript Received: 4 November 2003. | ||||||||||||
Subject Keywords: | Self-dual codes; weight enumerators; invariant ring; Clifford groups | ||||||||||||
Issue or Number: | 1 | ||||||||||||
Classification Code: | MSC (2000) Primary: 94B05, 13A50; Secondary: 94B60 | ||||||||||||
DOI: | 10.1002/mana.200310204 | ||||||||||||
Record Number: | CaltechAUTHORS:20171004-091341996 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171004-091341996 | ||||||||||||
Official Citation: | Nebe, G., Rains, E. M. and Sloane, N. J. A. (2004), Codes and invariant theory. Math. Nachr., 274-275: 104–116. doi:10.1002/mana.200310204 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 82035 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 04 Oct 2017 17:24 | ||||||||||||
Last Modified: | 15 Nov 2021 19:47 |
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