Some quantum MDS codes from GRS codes

ABSTRACT

The construction of quantum maximum-distance-separable (MDS) codes has become one of the major goals in quantum coding theory. In this paper, we construct several classes of Hermitian self-orthogonal generalized Reed–Solomon codes. Based on these classical MDS codes, we obtain several new classes of quantum MDS codes with large minimum distance. It turns out that these constructed quantum MDS codes have fewer constraints on the selection of code length, and in some cases, have larger minimum distance than previous literature. Notably, some of the distance parameters of our codes are greater than $\left(q/2\right)+1$.

KEYWORDS:

• Quantum MDS codes
• generalized Reed–Solomon codes
• Hermitian self-orthogonal

MATHEMATICS SUBJECT CLASSIFICATION:

• 94B60

Acknowledgments

We are grateful to the anonymous referees for useful comments and suggestions that improved the presentation and quality of this paper.

Availability of data and materials

The datasets supporting the conclusions of this article are included within the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 12171114).