New Quantum MDS codes from Hermitian self-orthogonal generalized Reed-Solomon codes

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.