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RT distance and weight distributions of Type 1 constacyclic codes of length 4*p*^{s} over 𝔽_{p}m[u] / <u^{a}>

RT distance and weight distributions of Type 1 constacyclic codes of length 4*p ^{s}* over 𝔽

_{p}m[u] / <u

^{a}>

For any odd prime p such that p^{m} ≡ 1 (mod 4), the class of Λ -constacyclic codes of length 4*p ^{s}* over the finite commutative chain ring , for all units Λ of ℛ

_{a}that have the form Λ = Λ

_{0}+uΛ

_{1}+ · · ·+u

^{a-1}Λ

_{a−1}, where Λ

_{0},Λ

_{1}, ...,Λ

_{a−1}∈ F

_{pm}, Λ

_{0}≠ 0, Λ

_{1}≠ 0 , is investigated. If the unit Λ is a square, each Λ -constacyclic code of length 4

*p*is expressed as a direct sum of a −λ-constacyclic code and a λ -constacyclic code of length 2

^{s}*p*. In the main case that the unit Λ is not a square, we show that any nonzero polynomial of degree < 4 over F

^{s}_{pm}is invertible in the ambient ring and use it to prove that the ambient ring is a chain ring with maximal ideal ⟨x

^{4}− λ

_{0}⟩, 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.