On Constacyclic codes over ℤpm

Let p be a prime number, m ≥ 2 a positive integer, and λ a unit of R = ℤ_p(m), the ring of integers modulo p^m. Let N = p^kn with gcd(p, n) = 1. In this work, we give a simple and short proof that the quotient ring R[X]/ <; X^N - (1 + λp) > is a principal ring. This allow us to study (1 + λp)-constacyclic codes of arbitrary length and give a characterization of self-dual (1 + λp)-constacyclic codes over ℤ_p(m).