Z₂Z₄-additive cyclic codes, generator polynomials and dual codes
Borges, J. (Joaquim) (Joaquim) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Fernández Córdoba, Cristina (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Ten-Valls, Roger (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)

Date:	2014
Abstract:	A Z₂Z₄-additive code C ⊆ Zα2 × Zβ₄ is called cyclic code if the set of coordinates can be partitioned into two subsets, the set of Z₂ and the set of Z₄ coordinates, such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the Z₄[x]-module Z₂[x]/(x^α − 1) × Z₄ [x]/(x^β − 1). The parameters of a Z₂Z₄-additive cyclic code are stated in terms of the degrees of the generator polynomials of the code. The generator polynomials of the dual code of a Z₂Z₄-additive cyclic code are determined in terms of the generator polynomials of the code C.
Grants:	Ministerio de Ciencia e Innovación TIN2013-40524-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Capítol de llibre
Subject:	Binary cyclic codes ; Duality ; Quaternary cyclic codes ; Z₂Z₄-additive cyclic codes
Published in:	Proceedings of Karatekin Mathematics Days. Çankiri, Turquia, 2014

15 p, 298.0 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Engineering > Combinatorics, Coding and Security Group (CCSG)
Contributions to meetings and congresses > Papers and communications > UAB papers and communications