Some New Constructions of Quantum MDS Codes
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It is an important task to construct quantum 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 codes and Hermitian construction. Most of our quantum MDS codes have minimum distance larger than q/2+1. Three of these six classes of quantum MDS codes have larger length than the ones constructed in 5 and 6, hence some of their results can be easily derived from ours via the propagation rule. Moreover, some quantum MDS codes of specific length can be seen as special cases of ours and the minimum distance of some known quantum MDS codes are also improved.
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