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 four 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：量子最大距离可分隔(MDS)码是量子码的重要类别。本文使用Hermitian自正交广义Reed-Solomon (GRS)码，构造了4类新$q$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。这些码的最小距离大于$q/2 + 1$。此外，我们的量子MDS码推广了先前的结果。