.  Consider a stabilizer code $\mathcal{S} =  \langle g_{0},g_{0},\cdots , g_{r} \rangle$ and $t$-flag circuits $\{ C(g_{0}),C(g_{0}), \cdots , C(g_{r}) \}$. For any set of $m$ stabilizer generators $\{ g_{i_{0}},\cdots ,g_{i_{m}} \}$ 