Abstract: Constacyclic codes over Rk were mainly discussed. It was proved that the image of a (1+uk)-constacyclic code of length n over Rk  under  is a binary quasi-cyclic of index 2k-1 and length 2kn. Rk[x]/(xn-(1+uk)) ring was studied. It was obtained that Rk,n is local when n=2m, that Rk,n is not local when n=2ms, where s>1 is an odd number.

Key words: Rk rings, Constacyclic codes, Gray maps