Skew Cyclic Codes Over A Class Of Finite Chain Rings And SGQC-codes

In this paper,we study skew cyclic codes over Rt=Fq+uFq+…+utFq of arbitrary length where q is power of prime p,and ut+1=0.We study the automorphism on this kind of finite chain rings and determine their automorphism groups.We characterize skew cyclic codes over Rt of length n as left Rt[x;Θ]-submodules of Rt[x;Θ]/<xn-1>,where Θ is an automorphism of Rt.We discuss the generators of skew cyclic codes over R1=Fq+ uFq,determine the minimal generating sets and the generators of dual codes.We study the generators of skew cyclic codes over R2=Fq+uFq+u2Fq,discuss the minimal generating sets and dual codes.Without restriction on t,we discuss the generators and minimal generating sets of skew cyclic codes over Rt=Fq+uFq+…+utFq in special three cases.Finally,we study the skew generalized quasi-cyclic codes over R1,and describe the minimal generating sets of a certain class of 1-generator SGQC-codes and the number of code words generated by the generators under certain conditions.