  It is an important task to construct quantum maximum-distance-separable (MDS)
codes with good parameters. In the present paper, we provide six new classes of
q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and
Hermitian construction. The minimum distances of our quantum MDS codes can be
larger than q/2+1 Three of these six classes of quantum MDS codes have longer
lengths than the ones constructed in [1] and [2], hence some of their results
can be easily derived from ours via the propagation rule. Moreover, some known
quantum MDS codes of specific lengths can be seen as special cases of ours and
the minimum distances of some known quantum MDS codes are also improved as
well.
