  For any constacyclic code over a finite commutative chain ring of length
coprime to the characteristic of the ring, we construct explicitly generator
polynomials and check polynomials, and exhibit a BCH bound for such
constacyclic codes. As a consequence, such constacyclic codes are principal.
Further, we get a necessary and sufficient condition that the cyclic codes over
a finite commutative principal ideal ring are all principal. This condition is
still sufficient for constacyclic codes over such rings being principal.
