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

2022/12/06 by Swati Bhardwaj, Bhardwaj, Swati, Mokshi Goyal +3
Computer Science · #11T71 #94B05 #94B15 #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2212.02821

openalex publication_date 2022/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q be a prime power and let R=\mathbbFq[u1,u2, ⋯, uk]/⟨ fi(ui),uiuj-ujui⟩ be a finite non-chain ring, where fi(ui), 1≤ i ≤ k are polynomials, not all linear, which split into distinct linear factors over \mathbbFq. 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 fi(ui), 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 gcd (n,q)≠ 1.

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