Open Access Kent State (OAKS)

The units of the chain ring ℛ_a = F_p^m [u]/〈u^a〉 = F_p^m + uF_p^m + ⋯ + u^a−1F_p^m are partitioned into a distinct types. It is shown that for any unit Λ of Type k, a unit λ of Type k∗ can be constructed, such that the class of λ-constacyclic of length p^s of Type k∗ codes is one-to-one correspondent to the class of Λ-constacyclic codes of the same length of Type k via a ring isomorphism. The units of ℛ_a of the form Λ = Λ₀ + u Λ₁ + ⋯ + u^a−1 Λ_a−1, where Λ₀, Λ₁, … , Λ_a−1 ∈ F_p^m, Λ₀ ≠ 0, Λ₁ ≠ 0, are considered in detail. The structure, duals, Hamming and homogeneous distances of Λ-constacyclic codes of length p^s over ℛ_a are established. It is shown that self-dual Λ-constacyclic codes of length p^s over ℛ_a exist if and only if a is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both α- and β-constacyclic over ℛ_a for different units α, β.