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Título: | Group code structures of affine-invariant codes |
Fecha de publicación: | ene-2011 |
Cita bibliográfica: | Journal of Algebra, 325, pp. 269-281 |
Palabras clave: | Coding theory Group codes Affine-invariant codes Permutation automorphism group Finite fields |
Resumen: | A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a nite group. In these realizations, the group algebra is identi ed with the ambient space, and the group elements with the coordinates of the ambient space. It is an obvious consequence of the de nition that every pr-ary a ne-invariant code of length pm, with p prime, can be realized as an ideal of the group algebra Fpr [(Fpm; +)], where (Fpm; +) is the underlying additive group of the eld Fpm with pm elements. In this paper we describe all the group code structures of an a ne-invariant code of length pm in terms of a family of maps from Fpm to the group of automorphisms of (Fpm; +). We also present a familly of non-obvious group code structures in an arbitrary a ne-invariant code. |
Autor/es principal/es: | Bernal Buitrago, José Joaquín Río Mateos, Ángel del Simón Pinero, Juan Jacobo |
Facultad/Departamentos/Servicios: | Matemáticas |
URI: | http://hdl.handle.net/10201/138725 |
DOI: | https://doi.org/10.1016/j.jalgebra.2010.08.021 |
Tipo de documento: | info:eu-repo/semantics/article |
Número páginas / Extensión: | 18 |
Derechos: | info:eu-repo/semantics/embargoedAccess Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
Descripción: | ©2024. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the Accepted, version of a Published Work that appeared in final form in Journal of Algebra. To access the final edited and published work see https://doi.org/10.1016/j.jalgebra.2010.08.021 |
Aparece en las colecciones: | Artículos: Matemáticas |
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