All α + uβ-constacyclic codes of length nps over Fpm+uFpm

Let Fpm be a finite field with cardinality pm and R=Fpm+uFpm with u2=0. We aim to determine all α+uβ-constacyclic codes of length nps over R, where α,β∈Fpm⁎, n,s∈N+ and gcd⁡(n,p)=1. Let α0∈Fpm⁎ and α0ps=α. The residue ring R[x]/〈xnps−α−uβ〉 is a chain ring with the maximal ideal 〈xn−α0〉 in the case that xn−α0 is irreducible in Fpm[x]. If xn−α0 is reducible in Fpm[x], we give the explicit expressions of the ideals of R[x]/〈xnps−α−uβ〉. Besides, the number of codewords and the dual code of every α+uβ-constacyclic code are provided.