OJAppS  Vol.2 No.4 B , December 2012
Cyclic codes of length 2k over Z8
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.

Cite this paper
nullGarg, A. and Dutt, S. (2012) Cyclic codes of length 2k over Z8. Open Journal of Applied Sciences, 2, 104-107. doi: 10.4236/ojapps.2012.24B025.
References
[1]   T. Abualrub and R. Oehmke, “Cyclic codes of length over Z4” Discrete Applied Mathematics 128 (2003) 3 – 9.

[2]   A.R. Calderbank, N.J.A. Sloane, Modular and p-adic cyclic codes, Designs Codes Cryptogr. 6 (1995) 21–35.

[3]   P. Kanwar, S.R. Lopez-Permouth, Cyclic codes over the integers modulo p, Finite Fields Appl. 3 (4) (1997) 334–1352.

[4]   F.J. MacWilliams, N.J.A. Sloane, The Theory of Error-Correcting Codes, Ninth impression, North-Holland, Amsterdam, 1977.

[5]   T. Blackford, Cyclic codes over Z4 of oddly even length, Discrete Applied Mathematics, Vol. 128 (2003) pp. 27–46.

[6]   Steven T. Dougherty, San Ling, Cyclic Codes Over Z4 of Even Length, Designs, Codes and Cryptography, vol 39, pp 127–153, 2006

[7]   Shi Minjia, Zhu Shixin. Cyclic Codes Over The Ring ZP2 Of Length pe. Journal Of Electronics (China), vol 25, no 5,(2008), 636-640.

[8]   I.S.Luthar, I.B.S.Passi. Algebra volume 2 Rings, Narosa Publishing House, first edition,2002.

 
 
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