  This paper is an expanded and more detailed version of our recent work in
which the Operator Quantum Error Correction formalism was introduced. This is a
new scheme for the error correction of quantum operations that incorporates the
known techniques - i.e. the standard error correction model, the method of
decoherence-free subspaces, and the noiseless subsystem method - as special
cases, and relies on a generalized mathematical framework for noiseless
subsystems that applies to arbitrary quantum operations. We also discuss a
number of examples and introduce the notion of ``unitarily noiseless
subsystems''.
