Constructions of quantum MDS codes

Hualu Liu; Xiusheng Liu

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arXiv · 2002.06040

Constructions of quantum MDS codes

Hualu Liu·Xiusheng Liu

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Abstract

Let $\mathbb{F}_q$ be a finite field with $q=p^{e}$ elements, where $p$ is a prime number and $e \geq 1$ 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 $\lceil\frac{q+2}{2}\rceil \leq k\leq q+1$, and $$[[n,2k-n,n-k+1]]_q$$ for $n\leq q $ and $ \lceil\frac{n}{2}\rceil \leq k\leq 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 \cite{Fang1}.

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Hualu Liu, Xiusheng Liu. 2020-02-14. Constructions of quantum MDS codes. https://arxiv.org/abs/2002.06040

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