The construction of quantum maximum distance separable (abbreviated to MDS) error-correcting codes has become one of the major concerns in quantum coding theory. In this paper, we further generalize the approach developed in the previous paper, and construct several new classes of Hermitian self-orthogonal generalized Reed-Solomon (GRS) codes. By employing these classical MDS codes, we obtain several classes of quantum MDS codes with large minimum distance. It turns out that our quantum MDS codes exhibited here have less constraints on the selection of code length and some of them have not been constructed before, and in some cases, have larger minimum distance than previous literature. Meanwhile, about half of the distance parameters of our codes are greater than $\frac{q}{2}+1$.

量子最大距离可分（简称MDS）纠错码的构建已成为量子编码理论的主要关注点之一。在本文中，我们进一步概括了前一篇论文中开发的方法，并构造了几个新的 Hermitian 自正交广义 Reed-Solomon (GRS) 码。通过使用这些经典的MDS码，我们得到了几类最小距离大的量子MDS码。事实证明，我们在这里展示的量子 MDS 代码对代码长度选择的限制较少，并且其中一些代码之前没有构建过，并且在某些情况下，比以前的文献具有更大的最小距离。同时，我们代码中大约一半的距离参数大于$\frac{q}{2}+1$.