New Quantum codes from constacyclic codes over a general non-chain ring

12/06/2022

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by   Swati Bhardwaj, et al.

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Let q be a prime power and let ℛ=𝔽_q[u_1,u_2, ⋯, u_k]/⟨ f_i(u_i),u_iu_j-u_ju_i⟩ be a finite non-chain ring, where f_i(u_i), 1≤ i ≤ k are polynomials, not all linear, which split into distinct linear factors over 𝔽_q. We characterize constacyclic codes over the ring ℛ and study quantum codes from these. As an application, some new and better quantum codes, as compared to the best known codes, are obtained. We also prove that the choice of the polynomials f_i(u_i), 1 ≤ i ≤ k is irrelevant while constructing quantum codes from constacyclic codes over ℛ, it depends only on their degrees. It is shown that there always exists Quantum MDS code [[n,n-2,2]]_q for any n with (n,q)≠ 1.