Publication: Group code structures of affine-invariant codes
Authors
Bernal Buitrago, José Joaquín ; Río Mateos, Ángel del ; Simón Pinero, Juan Jacobo
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Publisher
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DOI
https://doi.org/10.1016/j.jalgebra.2010.08.021
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info:eu-repo/semantics/article
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
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.
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Citation
Journal of Algebra, 325, pp. 269-281
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2027-01-01
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