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.