Classification of cyclic codes over a non-Galois chain ring Zp[u]/〈u3〉

Abstract

We explicitly determine generators of cyclic codes over a non-Galois finite chain ring Zp[u]/〈u3〉 of length pk, where p is a prime number and k is a positive integer. We completely classify that there are three types of principal ideals of Zp[u]/〈u3〉 and four types of non-principal ideals of Zp[u]/〈u3〉, which are associated with cyclic codes over Zp[u]/〈u3〉 of length pk. We then obtain a mass formula for cyclic codes over Zp[u]/〈u3〉 of length pk. © 2019