RT distance and weight distributions of Type 1 constacyclic codes of length 4p^s over 𝔽_pm[u] / <u^a>

For any odd prime p such that p^m ≡ 1 (mod 4), the class of Λ -constacyclic codes of length 4p^s over the finite commutative chain ring , for all units Λ of ℛ_a that have the form Λ = Λ₀+uΛ₁+ · · ·+u^a-1Λ_a−1, where Λ₀,Λ₁, ...,Λ_a−1 ∈ F_p^m, Λ₀ ≠ 0, Λ₁ ≠ 0 , is investigated. If the unit Λ is a square, each Λ -constacyclic code of length 4p^s is expressed as a direct sum of a −λ-constacyclic code and a λ -constacyclic code of length 2p^s. In the main case that the unit Λ is not a square, we show that any nonzero polynomial of degree < 4 over F_p^m is invertible in the ambient ring  and use it to prove that the ambient ring  is a chain ring with maximal ideal ⟨x⁴ − λ₀⟩, where . As an application, the number of codewords and the dual of each λ-constacyclic code are provided. Furthermore, we get the Rosenbloom–Tsfasman (RT) distance and weight distributions of such codes. Using these results, the unique MDS code with respect to the RT distance is identified.