A Class of Constacyclic Codes over R + vR and Its Gray Image


We study (1 + 2v)-constacyclic codes overR + vR and their Gray images, where v2 + v = 0 and R is a finite chain ring with maximal ideal <λ> and nilpotency index e. It is proved that the Gray map images of a (1 + 2v)-constacyclic codes of length n over R + vR are distance-invariant linear cyclic codes of length 2n over R. The generator polynomials of this kind of codes for length n are determined, where n is relatively prime to p, p is the character of the field R/<λ> . Their dual codes are also discussed.

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D. Liao and Y. Tang, "A Class of Constacyclic Codes over R + vR and Its Gray Image," International Journal of Communications, Network and System Sciences, Vol. 5 No. 4, 2012, pp. 222-227. doi: 10.4236/ijcns.2012.54029.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. Wolfmann, “Negacyclic and Cyclic Codes over Z4,” IEEE Transactions on Information Theory, Vol.45, No. 7, 1999, pp. 2527-2532. doi:10.1109/18.296397
[2] H. Tapia-Recillas and G. Vega, “Some Constacyclic Codes over Z2k and Binary Quasi-Cyclic Codes,” Discrete Appl. Math.Vol. 128, No. 1, 2002, pp. 305-316. doi:10.1016/S0166-218X(02)00453-5
[3] H. Q. Dinh and S. R. Lopez-Permouth, “Cyclic and Negacyclic Codes over Finite Chain Rings,” I IEEE Transactions on Information Theory, Vol. 50, No. 8, 2004, pp. 1728-1744. d oi:10.1109/TIT.2004.831789
[4] H. Q. Dinh, “Negacyclic Codes of Length 2s over Galois Rings,” IEEE Transactions on Information Theory, Vol. 51, No. 12, 2005, pp. 4252-4262. doi:10.1109/TIT.2005.859284
[5] B. Yildiz and S. Karadenniz, “Linear Codes over F2 + uF2 + vF2 + uvF2,” Des.Codes Cryptogr. Vol. 54, No. 1, 2010, pp. 61-81.
[6] S. X. Zhu, Y. Wang and M. Shi, “Some Results on Cyclic Codes over F2 + vF2,” IEEE Transactions on Information Theory, Vol. 56, No. 4, 2010, pp. 1680-1684. doi:10.1109/TIT.2010.2040896
[7] Zhu, L. Wang, “A Class of Constacyclic Codes over Fp + vFp and Its Gray Image,” Discrete Mathematics, Vol. 311, No. 9, 2011, pp. 2677-2682. doi:10.1016/j.disc.2011.08.015
[8] H. Matsumura, “Commutative Ring with Identity,” Cambridge University Press, Cambridge, 1989.

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