2024/04/02 by Om Prakash, Shikha Patel, Prakash, Om +3
Computer Science · #12L05 #16Z05 #94B05 #94B15 #94B35 #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography
paper · pdf · doi:10.48550/arxiv.2404.01904
openalex publication_date 2024/04/02 · openalex created_date 2024/04/05 · openalex updated_date 2026/07/28
Let \mathbbFq be a finite field of q=pm elements where p is a prime and m is a positive integer. This paper considers (γ,Δ)-cyclic codes over a class of finite non-chain commutative rings \mathscrRq,s=\mathbbFq[v1,v2,…,vs]/⟨ vi-vi2,vivj=vjvi=0⟩ where γ is an automorphism of \mathscrRq,s, Δ is a γ-derivation of \mathscrRq,s and 1≤ i≠ j≤ s for a positive integer s. Here, we show that a (γ,Δ)-cyclic code of length n over \mathscrRq,s is the direct sum of (θ,\Im)-cyclic codes of length n over \mathbbFq, where θ is an automorphism of \mathbbFq and \Im is a θ-derivation of \mathbbFq. Further, necessary and sufficient conditions for both (γ,Δ)-cyclic and (θ,\Im)-cyclic codes to contain their Euclidean duals are established. Then, we obtain many quantum codes by applying the dual containing criterion on the Gray images of these codes. These codes have better parameters than those available in the literature. Finally, the encoding and error-correction procedures for our proposed quantum codes are discussed.