Quantum codes from a class of constacyclic codes over finite commutative rings

Let p be an odd prime, and kk be an integer such that gcd(k, p) = 1. Using pairwise orthogonal idempotents γ₁, γ₂, γ₃ of the ring ℛ = 𝔽_p[u]/〈u^k+1−u〉, with γ₁ + γ₂ + γ₃ = 1, ℛ is decomposed as ℛ = γ₁ℛ ⊕ γ₂ℛ ⊕ γ₃ℛ, which contains the ring R = γ₁𝔽_p ⊕ γ₂𝔽_p ⊕ γ₃𝔽_p as a subring. It is shown that, for λ₀, λ_k ∈ 𝔽_p, λ₀+u^kλ_k ∈ R, and it is invertible if and only if λ₀ and λ₀ + λ_kare units of 𝔽_p. In such cases, we study (λ₀+u^kλ_k)-constacyclic codes over RR. We present a direct sum decomposition of (λ₀ + u^kλ_k)-constacyclic codes and their duals, which provides their corresponding generators. Necessary and sufficient conditions for a (λ₀ + u^kλ_k)-constacyclic code to contain its dual are obtained. As an application, many new quantum codes over 𝔽_p, with better parameters than existing ones, are constructed from cyclic and negacyclic codes over R.