Codes over Z_m

In a previous paper (Codes over certain rings, Inform. Contr. 20, 396–404) Blake defined codes over Zm, the integers modulo m, if m is the product of distinct primes, and remarked that no codes were available over Zpn if n > 1, since Zpn is not a semisimple ring. We show that codes over Zpn can be described in terms of codes over Zp and thus are able to describe the codes over Zm for any positive m.