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Título: | An intrinsical description of group codes |
Fecha de publicación: | ene-2009 |
Editorial: | Springer |
Cita bibliográfica: | Designs, codes and Cryptography Volume 51, pages 289–300, (2009) |
Palabras clave: | Linear code Group codes Reed-Muller codes |
Resumen: | A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism FG → Fn which maps G to the standard basis of Fn. Many classical linear codes have been shown to be group codes. In this paper we obtain a criterion to decide when a linear code is a group code in terms of its intrinsical properties in the ambient space Fn, which does not assume an “a priori” group algebra structure on Fn. As an application we provide a family of groups (including metacyclic groups) for which every two-sided group code is an abelian group code. It is well known that Reed-Solomon codes are cyclic and its parity check extensions are elementary abelian group codes. These two classes of codes are included in the class of Cauchy codes. Using our criterion we classify the Cauchy codes of some lengths which are left group codes and the possible group code structures on these codes. |
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/10201/138712 |
DOI: | https://doi.org/10.1007/s10623-008-9261-z |
Tipo de documento: | info:eu-repo/semantics/article |
Número páginas / Extensión: | 12 |
Derechos: | info:eu-repo/semantics/embargoedAccess |
Descripción: | ©2009. “Once the embargo has passed this document Will be 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 Designs, Codes and Cryptography. To access the final edited and published work see https://doi.org/10.1007/s10623-008-9261-z |
Aparece en las colecciones: | Artículos: Matemáticas |
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