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 quantum MDS codes. The 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。本文通过使用埃尔米特自正交广义Reed-Solomon（简称GRS）码，构造了四类新的量子MDS码。我们构造的量子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码推广了已有结论。