Z2Z4-Additive Cyclic Codes : Kernel and Rank
Borges, Joaquim (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Dougherty, Steven T. (University of Scranton. Department of Mathematics)
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:	2019
Abstract:	A Z(2)Z(4)-additive code C subset of Z(2)(alpha) x Z(4)(beta) is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z(2) coordinates and the set of Z(4) coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. Let Phi(C) be the binary Gray map image of C. We study the rank and the dimension of the kernel of a Z(2)Z(4)-additive cyclic code C, that is, the dimensions of the binary linear codes and ker (Phi(C)). We give upper and lower bounds for these parameters. It is known that the codes and ker(Phi (C)) are binary images of Z(2)Z(4)-additive codes that we denote by R(C) and K(C), respectively. Moreover, we show that R(C) and K(C) are also cyclic and determine the generator polynomials of these codes in terms of the generator polynomials of the code C.
Grants:	Ministerio de Ciencia e Innovación TIN2016-77918-P
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Gray map ; Kernel ; Rank ; Z2 Z4-additive cyclic codes
Published in:	IEEE transactions on information theory, Vol. 65, Issue 4 (April 2019) , p. 2119-2127, ISSN 1557-9654

DOI: 10.1109/TIT.2018.2870891

Postprint 15 p, 406.9 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Engineering > Combinatorics, Coding and Security Group (CCSG)
Articles > Research articles
Articles > Published articles