It is important task to construct quantum maximum-distance-separable (MDS for short) codes with good parameters. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct four new classes of quantum MDS codes. Our quantum MDS codes have flexible parameters. And the minimum distances of our quantum MDS codes can be larger than $q/2+1$. Furthermore, it turns out that our constructions generalize and improve some previous results.

翻译：构造具有良好参数的量子最大距离可分（简称MDS）码是一项重要任务。本文利用埃尔米特自正交广义里德-所罗门（简称GRS）码，构造了四类新的量子MDS码。我们的量子MDS码具有灵活的参数，且最小距离可以大于$q/2+1$。此外，我们的构造推广并改进了先前的一些结果。