  We describe generalizations of the Pauli group, the Clifford group and
stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We
examine a link with modular arithmetic, which yields an efficient way of
representing the Pauli group and the Clifford group with matrices over the
integers modulo d. We further show how a Clifford operation can be efficiently
decomposed into one and two-qudit operations. We also focus in detail on
standard basis expansions of stabilizer states.
