Z₂Z₄-additive cyclic codes, generator polynomials and dual codes
Borges, Joaquim Borges, 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 |
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Record created 2015-11-06, last modified 2024-05-22