On a class of (δ+αu²)-constacyclic codes over Fq[u]/ u⁴

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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 δ,α∈ Fq×, 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.