Kernels and ranks of cyclic and negacyclic quaternary codes
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)

Date:	2016
Abstract:	We study the rank and kernel of Z4 cyclic codes of odd length n and give bounds on the size of the kernel and the rank. Given that a cyclic code of odd length is of the form C = <fh, 2fg> , where fgh = x^n − 1, we show that <2f> ⊆ K(C) ⊆ C and C ⊆ R(C) ⊆ <fh, 2g> where K(C) is the preimage of the binary kernel and R(C) is the preimage of the space generated by the image of C. Additionally, we show that both K(C) and R(C) are cyclic codes and determine K(C) and R(C) in numerous cases. We conclude by usingthese results to determine the case for negacyclic codes as well.
Grants:	Ministerio de Ciencia e Innovación TIN2013-40524-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Cyclic codes ; Quaternary codes ; Rank ; Kernel
Published in:	Designs, codes and cryptography, Vol. 81, Issue 2 (Nov. 2016) , p. 347-364, ISSN 1573-7586

DOI: 10.1007/s10623-015-0163-6

Post-print 22 p, 1.2 MB

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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