Constructions of quantum MDS codes

2020/02/14 by Hualu Liu, Liu, Hualu, Xiusheng Liu +1 · 1 citation
Computer Science · #Quantum Computing Algorithms and Architecture #Coding theory and cryptography #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2002.06040

Abstract

Let \mathbbF_q be a finite field with q=p^e elements, where p is a prime number and e ≥ 1 is an integer. In this paper, by means of generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum maximum-distance-separable ( quantum MDS) codes with parameters [[q + 1, 2k-q-1, q-k+2]]_q for \lceil(q+2)/(2)\rceil ≤ k≤ q+1, and [[n,2k-n,n-k+1]]_q for n≤ q and \lceil(n)/(2)\rceil ≤ k≤ n. Our constructions improve and generalize some results of available in the literature. Moreover, we give an affirmative answer to the open problem proposed by Fang et al. in \citeFang1.

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