Abstract
Let Fq be a finite field of cardinality q, R=Fq[u]/<u4>=Fq+uFq+u2Fq+u3Fq (u4=0) which is a finite chain ring, and n be a positive integer satisfying gcd(q,n)=1. For any $\delta,\alpha\in \mathbb{F}_{q}^{\times}$, an explicit representation for all distinct (δ+αu2)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q=2m and δ=1, all self-dual (1+αu2)-constacyclic codes over R of odd length n are provided.
