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A Class of Constacyclic Codes over <i>R</i> + <i>vR</i> and Its Gray Image
College of Science, Huaihai Institute of Technology, Lianyungang, China
College of Science, Huaihai Institute of Technology, Lianyungang, China
- 1 College of Science, Huaihai Institute of Technology, Lianyungang, China
- 2 College of Science, Huaihai Institute of Technology, Lianyungang, China
International Journal of Communications, Network and System Sciences·Volume 05 (2012)·Pages 222–227·Published 18 April 2012·DOI10.4236/ijcns.2012.54029
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Abstract
We study (1 + 2 v )-constacyclic codes over R + vR and their Gray images, where v 2 + 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 + 2 v )-constacyclic codes of length n over R + vR are distance-invariant linear cyclic codes of length 2 n 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.
KeywordsFrobenius RingConstacyclic CodesGenerator PolynomialDual Codes
- 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
- 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
- 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
- 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
- B. Yildiz and S. Karadenniz, “Linear Codes over F2 + uF2 + vF2 + uvF2,” Des.Codes Cryptogr. Vol. 54, No. 1, 2010, pp. 61-81.
- 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
- 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
- H. Matsumura, “Commutative Ring with Identity,” Cambridge University Press, Cambridge, 1989.