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Pàgina inicial > Articles > Articles publicats > Kernels and ranks of cyclic and negacyclic quaternary codes |
Data: | 2016 |
Resum: | 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. |
Ajuts: | Ministerio de Ciencia e Innovación TIN2013-40524-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-691 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Cyclic codes ; Quaternary codes ; Rank ; Kernel |
Publicat a: | Designs, codes and cryptography, Vol. 81, Issue 2 (Nov. 2016) , p. 347-364, ISSN 1573-7586 |
Post-print 22 p, 1.2 MB |