Cyclic codes of length 2k over Z8 - Open Journal of Applied Sciences

OJAppS > Vol.2 No.4, December 2012

Open Journal of Applied Sciences

Volume 2, Issue 4 (December 2012)

ISSN Print: 2165-3917 ISSN Online: 2165-3925

Google-based Impact Factor: 0.92 Citations h5-index & Ranking

Cyclic codes of length 2^k over Z₈ ()

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Download as PDF (Size: 176KB) PP. 104-107

DOI: 10.4236/ojapps.2012.24B025 2,779 Downloads 4,955 Views Citations

Author(s)

Arpana Garg, Sucheta Dutt

Affiliation(s)

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

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

Share and Cite:

Garg, A. and Dutt, S. (2012) Cyclic codes of length 2^k over Z₈. Open Journal of Applied Sciences, 2, 104-107. doi: 10.4236/ojapps.2012.24B025.

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