Group code structures of affine-invariant codes

Bernal Buitrago, José Joaquín; Río Mateos, Ángel del; Simón Pinero, Juan Jacobo

Publication:
Group code structures of affine-invariant codes

dc.contributor.author	Bernal Buitrago, José Joaquín
dc.contributor.author	Río Mateos, Ángel del
dc.contributor.author	Simón Pinero, Juan Jacobo
dc.contributor.department	Matemáticas
dc.date.accessioned	2024-02-06T09:15:07Z
dc.date.available	2024-02-06T09:15:07Z
dc.date.issued	2011-01
dc.description	©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
dc.description.abstract	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.	es
dc.embargo.terms	2027-01-01
dc.format	application/pdf	es
dc.format.extent	18	es
dc.identifier.citation	Journal of Algebra, 325, pp. 269-281
dc.identifier.doi	https://doi.org/10.1016/j.jalgebra.2010.08.021
dc.identifier.uri	http://hdl.handle.net/10201/138725
dc.language	eng	es
dc.relation	DGI of Spain and Fundación Séneca	es
dc.rights	info:eu-repo/semantics/embargoedAccess	es
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 Internacional	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject	Coding theory	es
dc.subject	Group codes
dc.subject	Affine-invariant codes
dc.subject	Permutation automorphism group
dc.subject	Finite fields
dc.title	Group code structures of affine-invariant codes	es
dc.type	info:eu-repo/semantics/article	es
dspace.entity.type	Publication	es