Complete classification of (δ+αu2)-constacyclic codes over F2m[u]∕〈u4〉 of oddly even length

Let F2m be a finite field of cardinality 2m, R=F2m[u]∕〈u4〉 and n be an odd positive integer. For any δ,α∈F2m×, ideals of the ring R[x]∕〈x2n−(δ+αu2)〉 are identified as (δ+αu2)-constacyclic codes of length 2n over R. In this paper, an explicit representation and enumeration for all distinct (δ+αu2)-constacyclic codes of length 2n over R are presented.