中文摘要：

令R_（（p~m,k））=F_（p~m）[u]/〈u~k〉,其中p~（j-1）＋1≤k≤p~j、u~k=0、p为正素数、j为正整数.定义了从R_（（p~m,k））到F_（p~m）~（p~j）的一个新的Gray映射,得到了环R_（（p~m,k））上码长为任意长度N的线性（1＋u＋…＋u~（k-1））常循环码的Gray像是F_（p~m）上长为p~jN的保距线性循环码,并给出了Gray像的生成多项式,构造了F_3,F_5和F_7上的一些最优线性循环码.

英文摘要：

Let R_（（p~m,k））=F_（p~m）[u]/u~k,where p~（j-1）＋1≤k≤p~j and u~k=0 for some positive prime number pand positive integer j.A new Graymap from R_（（p~m,k））to F_（p~m）~（p~j） was defined.It was proved that the Gray image of a linear（1＋u＋…＋u~（k-1））constacyclic code of an arbitrary length N over R_（（p~m,k））is a distance invariant linear cyclic code of length p~jN over F_（p~m）.Moreover,the generator polynomial of the Gray image of such a constacyclic code was determined,and some optimal linear cyclic codes over F_3,F_5 and F_7 were constructed via the Gray map.