(u1)-constacyclic Codes of Arbitrary Lengths over the Ring Fq+uFq++uk1Fq

Let R denote the ring R=Fq+uFq++uk1Fq , and be an invertible element of R. By means of the theory of ring homomorphism, the generators of all these (u1)-constacyclic codes of an arbitrary length N over the ring R are obtained. It is proved thatR[x]xN+1u is principal. The number of these (u1)-constacyclic codes is determined. The generator polynomials of the highest-order torsion codes of all these (u1)-constacyclic codes are given. As a result, the Hamming distances of all these (u1)-constacyclic codes are obtained.