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On a Class of Constacyclic Codes of Length 4ps over 𝔽pm[u] / <ua>

Authors: 

Hai Q. Dinh, Bac T. Nguyen, Songsak Sriboonchitta

Source title: 
Algebra Colloquium, 26(2): 181-194, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

For any odd prime p such that pm ≡ 3 (mod 4), consider all units Λ of the finite commutative chain ring a that have the form Λ = Λ0 + uΛ1 + ⋯ + ua−1 Λa−1, where Λ0, Λ1, …, Λa−1 ∊ 𝔽pm, Λ0 ≠ 0, Λ1 ≠ 0. The class of Λ-constacyclic codes of length 4ps over ℛa is investigated. If the unit Λ is a square, each Λ-constacyclic code of length 4ps is expressed as a direct sum of a −λ-constacyclic code and a λ-constacyclic code of length 2ps. In the main case that the unit Λ is not a square, we prove that the polynomial x4 − λ0 can be decomposed as a product of two quadratic irreducible and monic coprime factors, where b. From this, the ambient ring d is proven to be a principal ideal ring, whose maximal ideals are e. We also give the unique self-dual Type 1 Λ-constacyclic codes of length 4ps over ℛa. Furthermore, conditions for a Type 1 Λ-constacyclic code to be self-orthogonal and dual-containing are provided.