Constructions of quantum MDS codes

02/14/2020

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by   Hualu Liu, et al.

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Let F_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 q+2/2≤ k≤ q+1, and [[n,2k-n,n-k+1]]_q for n≤ q and n/2≤ 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 <cit.>.