A class of constacyclic codes over Zpm

We study (1+λp)-constacyclic codes over Zpm of an arbitrary length, where λ is a unit of Zpm and m⩾2 is a positive integer. We first derive the structure of (1+λp)-constacyclic codes of length ps over GR(pm,a) and determine the Hamming and homogeneous distances of such constacyclic codes. These codes are then used to classify all (1+λp)-constacyclic codes over Zpm of length N=psn (n prime to p). In particular, the Gray images of (1+λp)-constacyclic codes over Zp2 are also discussed.