Skew Cyclic Codes over Fq+uFq+…+uk-1Fq
This paper studies a special class of linear codes, called skew cyclic codes, over the ring R= Fq+uFq+…+uk-1Fq, where q is a prime power. A Gray map ɸ from R to Fq and a Gray map ɸ' from Rn to Fnq are defined, as well as an automorphism Θ over R. It is proved that the images of skew cyclic codes over R under map ɸ' and Θ are cyclic codes over Fq, and they still keep the dual relation.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1340326Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 810
 Bonnecaze A, Udaya P. Cyclic codes and self-dual codes over (J). IEEE Trans Inform Theory, 1999, 45(4):1250-1255.
 Abualr T, Siap T. Cyclic codes over the rings and (J). Designs Codes and Cryptography, 2007, 42(3):273-287.
 Xu Xian-qi, Zhu Shi-xin. Skew cyclic codes over the ring (J). Journal of Hefei University of Technology, 2011, 34(9):1429-1432.
 Han Mu, Ye You-pei, Zhu Shi-xin. Cyclic codes over with length (J). Information Sciences, 2011, 181(4):926-934.
 Zhu Shi-xin, Li Ping, Wu Bo. A Class of Repeated-root Constacyclic Codes over the Ring (J). Journal of Electronics & Information Technology, 2008, 30(6):1394-1396.
 Qian Jian-fa, Ma Wen-ping. Constacyclic and cyclic codes over finite chain rings(J). Science Direct, 2009, 16(3):122-125.
 Li Fu-lin, Zhu Shi-xin. Quasi-cyclic codes over (J). Journal of Hefei University of Technology, 2009, 32(11):1766-1768.
 Ding Jian, Li Hong-ju. Construction of optimal codes with Homogenuous distance(J). Journal of University of Science and Technology of China, 2015, 45(7): 588-593.