Abstract: Let R(pm,k)=Fpm［u］/, where pj－1+1≤k≤pj and uk=0 for some positive prime number p and positive integer j. A new Gray map from R(pm,k) to Fpmpj was defined. It was proved that the Gray image of a linear (1+u+…+uk－1) constacyclic code of an arbitrary length N over R(pm,k) is a distance invariant linear cyclic code of length pjN over Fpm. 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.

Key words: linear code, cyclic code, constacyclic code, Gray map, optimal code