I am reading the paper Quantum error correction with only two extra qubits.
They say there that (in the section on the [[5, 1, 3]] code):
If a flag is raised or a syndrome is nontrivial, then the subsequent unflagged syndrome extractions are perfect, and suffice to correct either a possibly correlated error (if the flag is raised) or a weight ≤ 1 error (if no flag is raised but the syndrome is nontrivial)
What does "perfect extraction" mean in this context? Surely the unflagged circuits are just as susceptible to errors as the flagged ones, no? I hope it's not just a statement that says that since the distance is 1, and a single error was already raised, then we assume a-priori that the technique can only succeed if the unflagged round has exactly zero errors?
Thanks a lot in advance!!