A class of constacyclic codes of length 2pˢ over Fp^m[u,v] / ⟨u², v², uv − vu⟩

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Youssef Ahendouz
Ismail Akharraz

Abstract

Let p be an odd prime number. This paper investigates λ-constacyclic codes of length 2ps over the ring Rᵤ,ᵥ = Fpm[u,v] / ⟨u², v², uv − vu⟩, where λ = ψ + ρu + ηv + τuv, with ψ, ρ, η, τ ∈ Fpm, ψ ∈ F*pm, and ρ, η not both zero. When λ = μ² for some μ ∈ Rᵤ,ᵥ, the structures of all λ-constacyclic codes of length 2ps over Rᵤ,ᵥ are determined and can be expressed as the sum of a (−μ)-constacyclic code and a μ-constacyclic code of length ps. When λ is not a square, we classify these codes into four distinct types, provide the number of codewords for each type, and give the details of their dual codes.

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How to Cite
Ahendouz, Y., & Ismail Akharraz. (2024). A class of constacyclic codes of length 2pˢ over Fp^m[u,v] / ⟨u², v², uv − vu⟩. Gulf Journal of Mathematics, 17(2), 73-90. https://doi.org/10.56947/gjom.v17i2.1918
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