摘要
We study the structure of cyclic codes of length 2k?over Z8?for any natural number k.? It is known that cyclic codes of length 2k?over Z8?are 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 length?2k?over Z8?are generated as ideals by at most three elements.
We study the structure of cyclic codes of length 2k?over Z8?for any natural number k.? It is known that cyclic codes of length 2k?over Z8?are 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 length?2k?over Z8?are generated as ideals by at most three elements.
