  In 1997, Shor and Laflamme defined the weight enumerators for quantum
error-correcting codes and derived a MacWilliams identity. We extend their work
by introducing our double weight enumerators and complete weight enumerators.
The MacWilliams identities for these enumerators can be obtained similarly.
With the help of MacWilliams identities, we obtain various bounds for
asymmetric quantum codes.
