Fig. 4

Permutation of states and partition structure for two three-state channels following partition scheme \(\mathcal {I}_{1} = (\{1, 2\}, \{3, 5, 6\}, \{4\})\). a The rows and columns of the expanded generator matrix Q are both permuted following the order given by partition scheme \(\mathcal {I}_{1}\). b The block structure given by the thicker lines shows the the partitioning of the generator matrix following \(\mathcal {I}_{1}\). c The corresponding reduced matrix calculated from Eq. 23