On p490 of Nielsen and Chuang, 2010 the authors say that the preparation of the 'cat' state ($|000\ldots 0\rangle+|111\ldots 1\rangle$) is not Fault Tolerant. Below is my mock up of the diagram they draw for the preparation ($H$ and $C$-not-not *) and one part of the verification (the next two C-nots):
They then explain that this is not fault tolerant because a $Z$ error in the 'extra qubit' (i.e. that at the bottom of the diagram) propagates into two Z-errors in the ancilla qubits (the top three).
They they go onto say that this will not affect the Encoded data (I have not shown this in my diagram).
There are a couple of things that confuse me here. Firstly I cannot see how we get two $Z$-errors on the axillary qubits, Secondly even if we did get two $Z$-errors, surely this is a good thing as it will take our cat state back to the cat state? More the the crux of the issue - I cannot see what criterion they are using for fault tolerance here (I know what it means in the general case - i.e. unrecoverable error with probability no greater then $Cp^2$) and how there example violates it - Please can someone explain this to me.
*Not technical name - I couldn't find what it was actually called.