Also most commercial quadrature encoders has the following 6 outputs, A, A Not, B, B Not, Z, and Z Not.
I'm not sure if the "A" and "A Not" signals are just inverted (but otherwise aligned) of the same signal or if they are in fact a separate measurement/signal, but by comparing both signals you should be able to guard against some errors at least.
Not exactly. Many industrial encoders make you state the output type option you wish to have when you order them. The A and NOT A you describe is a full differential output option (and yes one is just the inversion of the other), best for long cable runs as it has better noise handling ability and double the signal to noise ratio over single ended outputs, however it has no 'error detecting' abilities over any of the other output options. Other optional output types are single ended output at various voltage levels (5v, 12v, 24v are common options) and finally open collector output option. Each option as an advantage for certain installations.