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Codes and invariant theory

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1002/mana.200310204DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/mana.200310204/abstractPublisherArticle
https://arxiv.org/abs/math/0311046arXivDiscussion Paper
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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