Abstract
Quantum maximal-distance-separable (MDS) codes that satisfy quantum Singleton bound with different lengths have been constructed by some researchers. In this paper, seven families of asymmetric quantum MDS codes are constructed by using constacyclic codes. We weaken the case of Hermitian-dual containing codes that can be applied to construct asymmetric quantum MDS codes with parameters $[[n,k,d_{z}/d_{x}]]_{q^{2}}$ . These quantum codes are able to correct quantum errors with greater asymmetry. Moreover, these quantum codes constructed in this paper are different from the ones in the literature.
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