  We investigate stabilizer codes with carrier qudits of equal dimension $D$,
an arbitrary integer greater than 1. We prove that there is a direct relation
between the dimension of a qudit stabilizer code and the size of its
corresponding stabilizer, and this implies that the code and its stabilizer are
dual to each other. We also show that any qudit stabilizer can be put in a
standard, or canonical, form using a series of Clifford gates, and we provide
an explicit efficient algorithm for doing this. Our work generalizes known
results that were valid only for prime dimensional systems and may be useful in
constructing efficient encoding/decoding quantum circuits for qudit stabilizer
codes and better qudit quantum error correcting codes.
