  Error operator bases for systems of any dimension are defined and natural
generalizations of the bit/sign flip error basis for qubits are given. These
bases allow generalizing the construction of quantum codes based on eigenspaces
of Abelian groups. As a consequence, quantum codes can be constructed from
linear codes over $\ints_n$ for any $n$. The generalization of the punctured
code construction leads to many codes which permit transversal (i.e. fault
tolerant) implementations of certain operations compatible with the error
basis.
