  We derive simple necessary and sufficient conditions under which a quantum
channel obtained from an arbitrary perturbation from the identity can be
reversed on a given code to the lowest order in fidelity. We find the usual
Knill-Laflamme conditions applied to a certain operator subspace which, for a
generic perturbation, is generated by the Lindblad operators. For a weak
interaction with an environment, the error space to be corrected is a subspace
of that spanned by the interaction operators, selected by the environment's
initial state.
