  This manuscript introduces various notions of k-locality of stabilizer codes
inherited from the associated stabilizer groups. A choice of generators for the
group leads to a Hamiltonian with the code in its groundspace, while a
Hamiltonian holding the code in its groundspace might be called effective if
its locality is less than that of a natural choice of generators (or any
choice). This paper establishes some conditions under which effective
Hamiltonians for stabilizer codes do not exist. Our results simplify in the
cases of Calderbank-Shor-Steane stabilizer codes and topologically-ordered
stabilizer codes arising from surface cellulations.
