Cyclic codes and minimal strong Gröbner bases over a principal ideal ring

We characterise minimal strong Gröbner bases of R[x], where R is a commutative principal ideal ring and deduce a structure theorem for cyclic codes of arbitrary length over R. When R is an Artinian chain ring with residue field and , we recover a theorem for cyclic codes of length n over R due to Calderbank and Sloane for .