A mass formula for cyclic codes over Galois rings of characteristic p3

We completely determine the explicit generators of cyclic codes of length pk(k≥1) over a Galois ring of characteristic p3 by their residue degree, and their two torsional degrees; there are exactly three types of cyclic codes, that is, one-generator, two-generator and three-generator cyclic codes. Using this classification result, we explicitly obtain a mass formula for cyclic codes of length pk over a Galois ring of characteristic p3.