Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct three new classes of $q$-ary quantum MDS codes. The $q$-ary quantum MDS codes we construct have larger minimum distances. And the minimum distance of these codes is greater than $q/2+1$. Furthermore, it turns out that our quantum MDS codes generalize the previous conclusions.

翻译：量子最大距离可分（简称MDS）码是一类重要的量子码。本文利用Hermitian自正交广义Reed-Solomon（简称GRS）码，构造了三类新的$q$元量子MDS码。我们构造的$q$元量子MDS码具有更大的最小距离，且这些码的最小距离大于$q/2+1$。此外，结果表明我们的量子MDS码推广了先前结论。