Cyclic codes of length 2^k over Z₈

Arpana Garg, Sucheta Dutt

Department of Applied Sciences PEC University of Technology, Sector - 12 Chandigarh. India.

DOI: 10.4236/ojapps.2012.24B025                

Abstract

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.

Keywords

Codes; Cyclic Codes; Ideal; Principal Ideal Ring

Conflicts of Interest

The authors declare no conflicts of interest.

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