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 five new classes of $q$-ary quantum MDS codes with minimum distance larger than $q\mathrm{/}2+1$. Furthermore, the parameters of our quantum MDS code cannot be obtained from the previous constructions.