An intrinsical description of group codes

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

Publication:
An intrinsical description of group 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	2024-02-06T09:14:38Z
dc.date.available	2024-02-06T09:14:38Z
dc.date.copyright	© 2008 Springer Science+Business Media, LLC
dc.date.issued	2009-01-06
dc.description.abstract	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.	es
dc.format	application/pdf	es
dc.format.extent	12	es
dc.identifier.citation	Designs, codes and Cryptography Volume 51, pages 289–300, (2009)
dc.identifier.doi	https://doi.org/10.1007/s10623-008-9261-z
dc.identifier.uri	http://hdl.handle.net/10201/138712
dc.language	eng	es
dc.publisher	Springer	es
dc.relation	DGI of Spain and Fundación Séneca de Murcia	es
dc.rights	info:eu-repo/semantics/openAccess	es
dc.rights	Attribution-NonCommercial-NoDerivates 4.0 International
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject	Linear code	es
dc.subject	Group codes
dc.subject	Reed-Muller codes
dc.title	An intrinsical description of group codes	es
dc.type	info:eu-repo/semantics/article	es
dc.type.version	info:eu-repo/semantics/acceptedVersión
dspace.entity.type	Publication	es