@@ -145,6 +145,18 @@ lint scripts `spellcheck.py`, `remove_trailing_block_apostrophes.py`, and
 `scripts/params/check_tableaux.py`.
 This is the routine-check list in `scripts/script_list_for_checking.txt`.
 
+**15. Explicit codes with \(d\leq 5\) get a small-distance parent.** An entry
+for one explicit code whose distance is at most five also lists a
+small-distance family as a parent. Use `small_distance_qubit_stabilizer` for
+qubit stabilizer codes only, `small_distance_quantum` for any other block
+quantum code, and `small_distance` for classical codes. Never list both quantum
+ones, since `small_distance_qubit_stabilizer` descends from
+`small_distance_quantum`. Omit the parent only when another parent already
+implies it (e.g., `hamming743` inherits `small_distance` through `hamming`),
+because the relation checkers flag the redundant edge. These parents feed the
+small-code lists (`list_small.yml`, `list_small_qubit_stabilizer.yml`,
+`list_small_quantum.yml`), so an explicit code without one drops out of them.
+
 ## Relation semantics
 
 - Relations are declared on the CHILD, in its `relations.parents` list; the
 
@@ -17,7 +17,7 @@ description: |
   A nonlinear binary code consisting of the 10 weight-two five-bit strings, thereby providing an encoding for the decimal digits 0 through 9. 
 
 protection: |
-  Detects some single bit-flips as well as unidirectional errors using the fact that each codeword has weight two. The code fails for any sequence of flips that maintains the constant weight.
+  Detects all single bit-flips as well as unidirectional errors using the fact that each codeword has weight two. The code fails for any sequence of flips that maintains the constant weight.
 
 realizations:
   - 'Used in the United States Postal Service''s POSTNET barcode system as well as the Postal Alphanumeric Encoding Technique (PLANET).'
@@ -31,12 +31,15 @@ relations:
     - code_id: binary_group_orbit
       detail: 'The two-in-five code is a binary group-orbit code with group \(S_5\).'
     - code_id: weight_two
+    - code_id: small_distance
 
 
 # Begin Entry Meta Information
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -38,7 +38,7 @@ relations:
     - code_id: construction_a
       detail: 'Using \term{Construction A}, the Julin-Golay codes yield non-lattice sphere-packings that hold records in 9 and 11 dimensions.'
     - code_id: q-ary_over_zq
-      detail: 'Julin codes can be obtained from simple nonlinear codes over \(\mathbb{Z}_4\) using the Gray map \cite{doi:10.1007/BF01388558}.'
+      detail: 'Simple nonlinear codes over \(\mathbb{Z}_4\) yield Julin codes under the Gray map \cite{doi:10.1007/BF01388558}.'
     - code_id: gray
       detail: 'Julin codes can be obtained from simple nonlinear codes over \(\mathbb{Z}_4\) using the Gray map \cite{doi:10.1007/BF01388558}.'
 
@@ -47,6 +47,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -40,8 +40,6 @@ relations:
       detail: 'The \([7,3,4]\) simplex code is the smallest difference-set cyclic code, arising from the lines of the projective plane \(PG(2,2)\) \cite[pg. 397]{preset:MacSlo}.'
     - code_id: small_distance
   cousins:
-    - code_id: incidence_matrix
-      detail: 'The \([7,3,4]\) simplex code is the smallest difference-set cyclic code, arising from the lines of the projective plane \(PG(2,2)\) \cite[pg. 397]{preset:MacSlo}.'
     - code_id: hamming743
       detail: 'The \([7,3,4]\) simplex code is the dual of the Hamming code and also its even-weight subcode \cite{preset:Feit,doi:10.1016/0012-365X(74)90085-5}.'
 
@@ -50,6 +48,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-09-21'
     - user_id: VictorVAlbert
 
@@ -23,8 +23,6 @@ relations:
       detail: 'Extended Hamming codes are RM\((m-2,m)\) codes.'
     - code_id: small_distance
   cousins:
-    - code_id: karlin
-      detail: 'The extended Hamming code is equivalent to the Karlin double circulant code for \(m=3\) \cite[Ch. 16]{preset:MacSlo}.'
     - code_id: univ_opt_q-ary
       detail: 'Several extended Hamming codes are LP universally optimal codes \cite{arxiv:1212.1913}.'
     - code_id: biorthogonal
@@ -40,6 +38,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -48,8 +48,6 @@ relations:
   cousins:
     - code_id: univ_opt_q-ary
       detail: 'Binary Hamming codes and several of their extended, punctured, and shortened versions are LP universally optimal codes \cite{arxiv:1212.1913}.'
-    - code_id: binary_quad_residue
-      detail: 'The \([7,4,3]\) Hamming code is a binary quadratic-residue code \cite[Ex. 3.2.10]{preset:HKSclass}.'
     - code_id: constantin_rao
       detail: 'The nonlinear CR codes for \(G = \mathbb{Z}_2^r\) reduce to Hamming codes at lengths \(n = 2^r - 1\) \cite{preset:Klove81}; see Ref. \cite{arxiv:1310.7536}.'
     - code_id: extended_hamming
@@ -64,6 +62,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert
 
@@ -39,7 +39,7 @@ relations:
   parents:
     - code_id: hamming
     - code_id: binary_quad_residue
-      detail: 'The \([7,4,3]\) Hamming code is a quadratic-residue code with generator polynomial \(1+x+x^3\) \cite{preset:MacSlo}.'
+      detail: 'The \([7,4,3]\) Hamming code is a quadratic-residue code with generator polynomial \(1+x+x^3\) \cite{preset:MacSlo}\cite[Ex. 3.2.10]{preset:HKSclass}.'
   cousins:
     - code_id: incidence_matrix
       detail: 'The \([7,4,3]\) Hamming code parity-check matrix corresponds to points in the Fano plane \(PG(2,2)\) \cite[Exam. 21.4.2]{preset:HKSgraphs}.'
@@ -57,6 +57,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-09-21'
     - user_id: VictorVAlbert
 
@@ -41,24 +41,24 @@ description: |
 relations:
   parents:
     - code_id: extended_hamming
-    - code_id: self_dual
-      detail: 'The \([8,4,4]\) extended Hamming code is the smallest doubly even self-dual code, and the unique Type II code of length \(8\) \cite[Rem. 4.3.10]{preset:HKSselfdual}.'
+    - code_id: karlin
+      detail: 'The \([8,4,4]\) extended Hamming code is equivalent to the Karlin double circulant code for \(m=3\) \cite[Ch. 16]{preset:MacSlo}.'
     - code_id: biorthogonal
       detail: 'The \([8,4,4]\) extended Hamming code is the first-order RM\((1,3)\) code.'
   cousins:
     - code_id: group
       detail: 'The \([8,4,4]\) extended Hamming code is a group-algebra code for the group \(\mathbb{Z}_2 \times \mathbb{Z}_4\) \cite{arxiv:1912.09167}.'
     - code_id: binary_quad_residue
       detail: 'The \([8,4,4]\) extended Hamming code is an extended quadratic-residue code \cite{preset:MacSlo}.'
-    - code_id: divisible
-      detail: 'The \([8,4,4]\) extended Hamming code is the smallest doubly even self-dual code, and the unique Type II code of length \(8\) \cite[Rem. 4.3.10]{preset:HKSselfdual}.'
 
 
 
 # Begin Entry Meta Information
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-09-21'
     - user_id: VictorVAlbert
 
@@ -41,7 +41,8 @@ notes:
 
 relations:
   parents:
-    - code_id: q-ary_linear
+    - code_id: griesmer
+      detail: 'The Griesmer bound implies the Singleton bound, and MDS codes attain both. For \(k\geq 2\), this follows because MDS codes have distance \(d\leq q\) \cite[Ch. 11]{preset:MacSlo}.'
     - code_id: optimal_lrc
       detail: 'The generalized Singleton bound becomes the Singleton bound for \(k=r\), so optimal LRCs with that constraint are MDS.'
     - code_id: univ_opt_q-ary
@@ -61,6 +62,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: MarkusGrassl
 
@@ -54,10 +54,10 @@ relations:
       detail: 'The hexacode is a triply extended RS code \cite[pg. 82]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: lexicographic
       detail: 'Hexacodewords can be arranged in an order from smallest to largest, with each codeword differing at four places from the next \cite{manual:{R. A. Wilson, On lexicographic codes of minimal distance 4, Atti Sem. Mat. Fis. Univ. Modena 33 (1984)}}\cite[pg. 327]{preset:MacSlo}.'
-    - code_id: small_distance
-  cousins:
     - code_id: mds
       detail: 'The hexacode is an MDS code \cite[Exer. 578]{doi:10.1017/CBO9780511807077}.'
+    - code_id: small_distance
+  cousins:
     - code_id: q-ary_quad_residue
       detail: 'The hexacode is the smallest example of an extended quadratic-residue code of Type \(4^H\) \cite[Sec. 2.4.6]{doi:10.1007/3-540-30731-1}\cite[Exer. 363]{doi:10.1017/CBO9780511807077}.'
     - code_id: q-ary_hamming
@@ -79,6 +79,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-13'
     - user_id: VictorVAlbert
       date: '2026-06-08'
     - user_id: VictorVAlbert