2018/03/18 by Weijun Fang, Fang, Weijun, Fang‐Wei Fu +1 · 2 citations
Computer Science · #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.1803.06602
openalex publication_date 2018/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p be a prime and let q be a power of p. In this paper, by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes, we construct two new classes of quantum maximum-distance- separable (MDS) codes with parameters [[tq, tq-2d+2, d]]q for any 1 ≤ t ≤ q, 2 ≤ d ≤ \lfloor (tq+q-1)/(q+1)\rfloor+1, and [[t(q+1)+2, t(q+1)-2d+4, d]]q for any 1 ≤ t ≤ q-1, 2 ≤ d ≤ t+2 with (p,t,d) ≠ (2, q-1, q). Our quantum codes have flexible parameters, and have minimum distances larger than (q)/(2)+1 when t > (q)/(2). Furthermore, it turns out that our constructions generalize and improve some previous results.