Construction of quantum MDS codes from generalized Reed–Solomon codes

Quantum maximum-distance-separable (MDS) codes play an important role in the quantum codes. The previous quantum MDS codes had been constructed according to [Formula: see text] is odd or even. However, such classification omits to consider some special categories of quantum MDS codes. Because of this, we will discuss the other classifications of [Formula: see text]. In this paper, we construct some new [Formula: see text]-ary quantum MDS codes from generalized Reed–Solomon codes by using Hermitian construction, and prove that these quantum MDS codes have minimum distance greater than [Formula: see text], where [Formula: see text].