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has been cited by the following article:
TITLE: Cyclic codes of length 2k over Z8
AUTHORS: Arpana Garg, Sucheta Dutt
KEYWORDS: Codes; Cyclic Codes; Ideal; Principal Ideal Ring
JOURNAL NAME: Open Journal of Applied Sciences, Vol.2 No.4B, January 15, 2013
ABSTRACT: We study the structure of cyclic codes of length 2kover Z8for any natural number k. It is known that cyclic codes of length 2kover Z8are ideals of the ring R=Z8[X]/. In this paper we prove that the ring R=Z8[X]/ is a local ring with unique maximal ideal, thereby implying that R is not a principal ideal ring. We also prove that cyclic codes of length2kover Z8are generated as ideals by at most three elements.