Constacyclic codes of arbitrary lengths over ring $$Z_{p^m } + vZ_{p^m }$$
Tóm tắt
By constructing a Gray map, constacyclic codes of arbitrary lengths over ring
$$R = Z_{p^m } + vZ_{p^m }$$
are studied, where v
2 = v The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular, (1+(v+1)αp)-constacyclic codes over R are classified in terms of generator polynomial, where α is a unit of
$$Z_{p^m }$$
.
Tài liệu tham khảo
H. Q. Dinh and S. R. López-Permouth. Cyclic and negacyclic codes over finite chain rings. IEEE Transactions on Information Theory, 50(2004)8, 1728–1744.
H. Q. Dinh. Constacyclic codes of length p s over \(F_{p^m } + uF_{p^m }\). Journal of Algebra, 324(2010)5, 940–950.
Liang Hua and Tang Yuansheng. Cyclic codes over ring \(F_{p^m } + uF_{p^m }\). Application Research of Computers, 27(2010)6, 2026–2027.
Li Ping and Zhu Shixin. Cyclic codes of arbitrary lengths over the ring F q + uF q . Journal of University of Science and Technology of China, 38(2008)12, 1392–1396.
T. A. GulIiver and M. Harada. Codes over F 3 + uF 3 and improvements to the bounds on ternary linear codes. Designs Codes and Cryptography, 22 (2001)1, 89–96.
Zhu Shixin, Wang Yu and Shi Minjia. Some results on cyclic codes over F 2+vF 2. IEEE Transactions on Information Theory, 56(2010)4, 1680–1684.
Zhang Guanghui and Chen Bocong. Constacyclic Codes over F p+vF p arXiv preprint arXiv:1301.0669, 2013.
Zhu Shixin and Wang Liqi. A class of constacyclic codes over F p+vF p and its Gray image. Discrete Mathematics, 311(2011)23, 2677–2682.
Liao Dajian and Tang Yuansheng. A class of constacyclic codes over R+vR and its Gray image. International Journal of Communications, Network & System Sciences, 5(2012)4, 222–227.
A. Sălăgean. Repeated-root cyclic and negacyclic codes over a finite chain ring. Discrete Applied Mathematics, 154(2006)2, 413–419.
Zhu Shixin and Kai Xiaoshan. A class of constacyclic codes over \(Z_{p^m }\). Finite Fields and Their Applications, 16(2010)4, 243–254.
Zhu Shixin and Kai Xiaoshan. Dual and self-dual negacyclic codes of even length over \(Z_{2^a }\). Discrete Mathematics, 309(2009)8, 2382–2391.