Codes and Invariant Theory

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dc.creatorNebe, Gabriele
dc.creatorRains, E. M.
dc.creatorSloane, N. J. A.
dc.date2003-11-04
dc.date.accessioned2026-07-07T08:18:15Z
dc.date.available2026-07-07T08:18:15Z
dc.descriptionThe 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 the integers modulo a power of 2, and self-dual codes over the noncommutative ring $\F_q + \F_q u$, where $u^2 = 0$..
dc.identifierhttps://arxiv.org/abs/math/0311046
dc.identifierhttp://arxiv.org/abs/math/0311046
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134366
dc.subjectNumber Theory
dc.subjectInformation Theory
dc.subject94B05, 13A50, 94B60
dc.titleCodes and Invariant Theory
dc.typetext

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