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On a Class of Constacyclic Codes of Length 4*p*^{s} over 𝔽_{p}m[u] / <u^{a}>

On a Class of Constacyclic Codes of Length 4*p ^{s}* over 𝔽

*[u] / <u*

_{p}m^{a}>

For any odd prime p such that *p ^{m}* ≡ 3 (mod 4), consider all units Λ of the finite commutative chain ring that have the form Λ = Λ

_{0}+ uΛ

_{1}+ ⋯ + u

^{a−1}Λ

_{a−1}, where Λ

_{0}, Λ

_{1}, …, Λ

_{a−1}∊ 𝔽

*m, Λ*

_{p}_{0}≠ 0, Λ

_{1}≠ 0. The class of Λ-constacyclic codes of length 4

*p*over ℛ

^{s}_{a}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 prove that the polynomial x

^{s}^{4}− λ

_{0}can be decomposed as a product of two quadratic irreducible and monic coprime factors, where . From this, the ambient ring is proven to be a principal ideal ring, whose maximal ideals are . We also give the unique self-dual Type 1 Λ-constacyclic codes of length 4

*p*over ℛ

^{s}_{a}. Furthermore, conditions for a Type 1 Λ-constacyclic code to be self-orthogonal and dual-containing are provided.