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 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.