(1+λu)-Constacyclic codes over Fp[u]/〈um〉

Journal of the Franklin Institute - Tập 347 - Trang 751-762 - 2010
Xiaoshan Kai1,2, Shixin Zhu1,2, Ping Li1,2
1School of Mathematics, Hefei University of Technology, Hefei 230009, Anhui, PR China
2National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, PR China

Tài liệu tham khảo

Abualrub, 2009, Constacyclic codes over F2 + uF2, Journal of the Franklin Institute, 346, 520, 10.1016/j.jfranklin.2009.02.001 Abualrub, 2007, Cyclic codes over the rings Z2+uZ2 and Z2+uZ2+u2Z2, Designs, Codes and Cryptography, 42, 273, 10.1007/s10623-006-9034-5 Amarra, 2008, On (1−u)-cyclic codes over Fpk+uFpk, Applied Mathematics Letters, 21, 1129, 10.1016/j.aml.2007.07.035 (Online). Available: 〈http://www.codetables.de/〉. Bachoc, 1997, Application of coding theory to the construction of modular lattices, Journal of Combinatorial Theory Series A, 78, 92, 10.1006/jcta.1996.2763 Blackford, 2003, Negacyclic codes over Z4 of even length, IEEE Transactions on Information Theory, 49, 1417, 10.1109/TIT.2003.811915 Bonnecaze, 1999, Cyclic codes and self-dual codes over F2 + uF2, IEEE Transactions on Information Theory, 45, 1250, 10.1109/18.761278 Dinh, 2005, Negacyclic codes of length 2s over Galois rings, IEEE Transactions on Information Theory, 51, 4252, 10.1109/TIT.2005.859284 Dinh, 2009, Constacyclic codes of length 2s over Galois extension rings of F2 + uF2, IEEE Transactions on Information Theory, 55, 1730, 10.1109/TIT.2009.2013015 Dougherty, 1999, Type II Codes Over F2 + uF2, IEEE Transactions on Information Theory, 45, 32, 10.1109/18.746770 Gulliver, 2001, Codes over F3+uF3 and improvements to the bounds on ternary linear codes, Designs, Codes and Cryptography, 22, 89, 10.1023/A:1008355310919 Gulliver, 1999, Construction of optimal type IV self-dual codes over F2 + uF2, IEEE Transactions on Information Theory, 45, 2520, 10.1109/18.796394 Hammons, 1994, The Z4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Transactions on Information Theory, 40, 301, 10.1109/18.312154 Huffman, 2007, On the decomposition of self-dual codes over F2 + uF2 with an automorphism of odd prime order, Finite Fields and Their Applications, 13, 681, 10.1016/j.ffa.2006.02.003 Kanwar, 1997, Cyclic codes over the integers modulo Zpm, Finite Fields and Their Applications, 3, 334, 10.1006/ffta.1997.0189 Ling, 2002, Zpk+1-linear codes, IEEE Transactions on Information Theory, 48, 2592, 10.1109/TIT.2002.801473 McDonald, 1974 Norton, 2000, On the structure of linear and cyclic codes over a finite chain ring, Applicable Algebra in Engineering, Communication and Computing, 10, 489 Qian, 2006, (1+u)-constacyclic and cyclic codes over F2+uF2, Applied Mathematics Letters, 19, 820, 10.1016/j.aml.2005.10.011 Saˇlaˇgean, 2006, Repeated-root cyclic and negacyclic codes over finite chain rings, Discrete Applied Mathematics, 154, 413, 10.1016/j.dam.2005.03.016 Siap, 2000, New linear codes over F3 and F5 and improvements on bounds, Designs, Codes and Cryptography, 21, 223, 10.1023/A:1008356131869 Siap, 2002, New linear codes over F5 obtained by tripling method and improvements on bounds, IEEE Transactions on Information Theory, 48, 2764, 10.1109/TIT.2002.802639 Tapia-Recillas, 2003, Some constacyclic codes over Z2k and binary quasi-cyclic codes, Discrete Applied Mathematics, 128, 305, 10.1016/S0166-218X(02)00453-5 Udaya, 1999, Decoding of cyclic codes over F2 + uF2, IEEE Transactions on Information Theory, 45, 2148, 10.1109/18.782165 Wolfmann, 2001, Binary images of cyclic codes over Z4, IEEE Transactions on Information Theory, 47, 1773, 10.1109/18.930917 Wolfmann, 1999, Negacyclic and cyclic codes over Z4, IEEE Transactions on Information Theory, 45, 2527, 10.1109/18.796397 Zhu, 2009, Dual and self-dual negacyclic codes of even length over Z2a, Discrete Mathematics, 309, 2382, 10.1016/j.disc.2008.05.013