diff --git a/codes/quantum/oscillators/stabilizer/lattice/gkp_concatenated.yml b/codes/quantum/oscillators/stabilizer/lattice/gkp_concatenated.yml
index 598662e60..223962f93 100644
--- a/codes/quantum/oscillators/stabilizer/lattice/gkp_concatenated.yml
+++ b/codes/quantum/oscillators/stabilizer/lattice/gkp_concatenated.yml
@@ -17,7 +17,7 @@ protection: |
 
 
 features:
-  rate: 'Recursively concatenating the \([[6,2,2]]\) and \([[4,2,2]]\) codes with GKP codes achieves the hashing bound of the displacement channel \cite{arxiv:1712.00294}. Concatenating Abelian LP codes with GKP codes can surpass the CSS Hamming bound \cite{arxiv:2111.07029}.'
+  rate: 'Recursively concatenating the \(C_6\) and \([[4,2,2]]\) codes with GKP codes achieves the hashing bound of the displacement channel \cite{arxiv:1712.00294}. Concatenating Abelian LP codes with GKP codes can surpass the CSS Hamming bound \cite{arxiv:2111.07029}.'
 
   general_gates:
     - 'Linear-optical computation \cite{arxiv:2408.04126}.'
@@ -40,9 +40,9 @@ relations:
     - code_id: quantum_repetition
       detail: 'Concatenating a three-qubit quantum repetition code with GKP codes can correct some two-bit-flip errors \cite{arxiv:1706.03011} (see also \cite{arxiv:2212.11397}).'
     - code_id: stab_4_2_2
-      detail: 'Recursively concatenating the \([[6,2,2]]\) and \([[4,2,2]]\) codes with GKP codes achieves the hashing bound of the displacement channel \cite{arxiv:1712.00294}.'
+      detail: 'Recursively concatenating the \(C_6\) and \([[4,2,2]]\) codes with GKP codes achieves the hashing bound of the displacement channel \cite{arxiv:1712.00294}.'
     - code_id: stab_6_2_2
-      detail: 'Recursively concatenating the \([[6,2,2]]\) and \([[4,2,2]]\) codes with GKP codes achieves the hashing bound of the displacement channel \cite{arxiv:1712.00294}.'
+      detail: 'Recursively concatenating the \(C_6\) and \([[4,2,2]]\) codes with GKP codes achieves the hashing bound of the displacement channel \cite{arxiv:1712.00294}.'
     - code_id: abelian_lifted_product
       detail: 'GKP codes have been concatenated with Abelian LP codes \cite{arxiv:2111.07029} that are in turn based on QC-LDPC codes \cite{doi:10.1109/TIT.2004.831841}.'
     - code_id: quantum_parity
diff --git a/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml b/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml
index 446f64b28..70140b4be 100644
--- a/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml
+++ b/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml
@@ -26,7 +26,7 @@ features:
     - 'Efficient decoder \cite{arxiv:2207.08826}.'
   fault_tolerance:
     - 'Syndrome measurement can be done with two ancillary flag qubits \cite{arxiv:1705.02329}.'
-    - 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \([[6,2,2]]\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826}.'
+    - 'Concatenations of quantum Hamming codes with the \([[4,2,2]]\) and \(C_6\) codes yield fault-tolerant quantum computation with constant space and quasi-polylogarithmic time overheads \cite{arxiv:2207.08826}.'
   threshold:
     - '\hyperref[topic:measurement-threshold]{Concatenated threshold} requiring constant-space and quasi-polylogarithmic time overhead \cite{arxiv:2207.08826}.'
 
diff --git a/codes/quantum/qubits/subsystem/qldpc/bbs/compass_model.yml b/codes/quantum/qubits/subsystem/qldpc/bbs/compass_model.yml
index cfe39294e..8138fb0eb 100644
--- a/codes/quantum/qubits/subsystem/qldpc/bbs/compass_model.yml
+++ b/codes/quantum/qubits/subsystem/qldpc/bbs/compass_model.yml
@@ -34,6 +34,7 @@ features:
 relations:
   parents:
     - code_id: subsystem_css
+    - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: rotated_surface
       detail: 'The surface-density compass code family interpolates between Bacon-Shor codes and rotated surface codes.'
diff --git a/codes/quantum/qubits/subsystem/qldpc/bbs/trapezoid.yml b/codes/quantum/qubits/subsystem/qldpc/bbs/trapezoid.yml
index aa3d05389..8f7ca8ff2 100644
--- a/codes/quantum/qubits/subsystem/qldpc/bbs/trapezoid.yml
+++ b/codes/quantum/qubits/subsystem/qldpc/bbs/trapezoid.yml
@@ -23,6 +23,7 @@ features:
 relations:
   parents:
     - code_id: bravyi_bacon_shor
+    - code_id: translationally_invariant_subsystem
   cousins:
     - code_id: iceberg
       detail: 'The trapezoid code family can be obtained from the \([[2m,2m-2,2]]\) error-detecting code by using some logical qubits as gauge qubits and imposing a two-dimensional qubit geometry \cite{arXiv:2412.06744}.'