Constacyclic codes of length (p^r, p^s) over mixed alphabets

Abstract

For any prime p and positive integer m, let R be the finite commutative ring Fpm+uFpm+vFpm+uvFpm, whereu2= 0 , v2= 0 and uv= vu. Let λ= λ1+ uλ2+ vλ3+ uvλ4 be a unit of R, where λ1,λ2,λ3,λ4∈Fpm and λ1≠ 0. We know that λ-constacyclic codes of length ps over R are exactly ideals of the ring R[x]⟨xps-λ⟩. For all possible values of λ, we study λ-constacyclic codes of length ps over R. We also extend structures of codes from single alphabet to mixed alphabet, and determine separable constacyclic codes of length (pr, ps) over FpmR.