  [0.0]{} ![(a) A 0-flag circuit for measuring the stabilizer $Z_{0}Z_{0}Z_{00}Z_{00}Z_{00}Z_{00}Z_{00}Z_{00}$ of the [$[\![00,0,0]\!]$]{} Hamming code. However a single fault on the fourth or fifth CNOT can lead to the error $Z_{00}Z_{00}Z_{00}Z_{00}$ on the data which is a logical fault. With the CNOT gates permuted as shown in (b), the [$[\![00,0,0]\!]$]{} satisfies the general flag 0-FTEC condition.](CircuitReichardt0.png "fig:"){width="\textwidth"}  [0.0]{} ![(a) A 0-flag circuit for measuring the stabilizer $Z_{0}Z_{0}Z_{00}Z_{00}Z_{00}Z_{00}Z_{00}Z_{00}$ of the [$[\![00,0,0]\!]$]{} Hamming code. However a single fault on the fourth or fifth CNOT can lead to the error $Z_{00}Z_{00}Z_{00}Z_{00}$ on the data which is a logical fault. With the CNOT gates permuted as shown in (b), the [$[\![00,0,0]\!]$]{} satisfies the general flag 0-FTEC condition.](CircuitReichardt0.png "fig:"){width="\textwidth"}  