CYCLIC CODES OVER Fq+uFq+vFq+uvFq

摘要

In this paper, by studying the polynomial ring R_n=(F_q+u F_q+vF_q+uvF_q)[x]/(x~n-1), cyclic codes over the ring R=F_q+u F_q+vF_q+uvF_q are discussed, where the ring R is not a finite chain ring. Finally, when q=2, let S=F_2+uF_2+vF_2+uvF_2, by studying the polynomial ring S_n=(F_2+uF_2+vF_2+uvF_2) [x]/(x~n-(1+u)) and using the corresponding relationship between the (1+u)-constacyclic codes over the ring S and the ideals in the ring S_n, (1+u)-constacyclic codes over the ring S are characterized.