New quantum MDS codes over finite fields

In this paper, we present three new classes of q-ary quantum MDS codes utilizing generalized Reed–Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some q-ary quantum MDS codes can be bigger than \(\frac{q}{2}+1\). Comparing to previous known constructions, the lengths of codes in our constructions are more flexible.