  In [Phys. Rev. A 58, 1833 (1998)] a family of polynomial invariants which
separate the orbits of multi-qubit density operators $\rho$ under the action of
the local unitary group was presented. We consider this family of invariants
for the class of those $\rho$ which are the projection operators describing
stabilizer codes and give a complete translation of these invariants into the
binary framework in which stabilizer codes are usually described. Such an
investigation of local invariants of quantum codes is of natural importance in
quantum coding theory, since locally equivalent codes have the same
error-correcting capabilities and local invariants are powerful tools to
explore their structure. Moreover, the present result is relevant in the
context of multipartite entanglement and the development of the
measurement-based model of quantum computation known as the one-way quantum
computer.
