~

valbert4 · valbert4 · commit 739dcbad9f43 · 2026-03-18T15:59:20.000-06:00
diff --git a/codes/classical/analog/sphere_packing/lattice/bw/lambda16.yml b/codes/classical/analog/sphere_packing/lattice/bw/lambda16.yml
@@ -26,6 +26,8 @@ relations:
       detail: 'The \(\Lambda_{16}\) Barnes-Wall lattice can be obtained from the Leech lattice by restricting to a fixed 16-dimensional subspace of an involution \cite[Ch. 4, pg. 131]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: biorthogonal
       detail: 'Applying Construction B to the first-order RM\((1,4)\) code yields the \(\Lambda_{16}\) Barnes-Wall lattice \cite[Ch. 4, pg. 130]{doi:10.1007/978-1-4757-6568-7}\cite[Exam. 10.7.2]{preset:EricZin}.'
+    - code_id: q-ary_repetition
+      detail: 'A Barnes-Wall \(\Lambda_{16}\) lattice can be obtained from the \([4,1,4]\) repetition code over \(\mathbb{F}_9\) via Quebbemann''s construction \cite[Ch. 8, pg. 219]{doi:10.1007/978-1-4757-6568-7}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/classical/analog/sphere_packing/lattice/coxeter_todd.yml b/codes/classical/analog/sphere_packing/lattice/coxeter_todd.yml
@@ -27,7 +27,9 @@ relations:
     - code_id: leech
       detail: 'The Coxeter-Todd lattice can be realized as a subset of the Leech lattice \cite[Ch. 4, pg. 128]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: hexacode
-      detail: 'The hexacode can be used to obtain the Coxeter-Todd \(K_{12}\) lattice \cite[Exam. 10.5.6]{preset:EricZin}.'
+      detail: 'The hexacode can be used to obtain the Coxeter-Todd \(K_{12}\) lattice \cite[Exam. 10.5.6]{preset:EricZin}\cite[Ch. 7, pg. 198]{doi:10.1007/978-1-4757-6568-7}.'
+    - code_id: q-ary_repetition
+      detail: 'Applying Construction \(B_c\) to the ternary repetition code of length \(6\) over the Eisenstein integers yields the Coxeter-Todd \(K_{12}\) lattice \cite[Ch. 7, pg. 200]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: self_dual_lattice
       detail: 'The Coxeter-Todd lattice is unimodular when defined as a complex lattice over the Eisenstein integers \cite[Ch. 4, pg. 128]{doi:10.1007/978-1-4757-6568-7}.'
 
diff --git a/codes/classical/analog/sphere_packing/lattice/dual/eeight.yml b/codes/classical/analog/sphere_packing/lattice/dual/eeight.yml
@@ -54,6 +54,8 @@ relations:
       detail: 'The \([8,4,4]\) extended Hamming code yields the \(E_8\) Gosset lattice via \term{Construction A} \cite[Exam. 10.5.2]{preset:EricZin}\cite[pg. 138]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: repetition
       detail: 'The \([8,1,8]\) repetition code can be used to obtain the \(E_8\) Gosset lattice \cite[Exam. 10.7.1]{preset:EricZin}.'
+    - code_id: witting_polytope
+      detail: 'The Voronoi cell of the \(E_8\) Gosset lattice is the dual of the Gosset \(4_{21}\) polytope \cite[Ch. 21, pg. 464]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: sharp_config
       detail: 'Several spherical sharp configurations are derived from the \(E_8\) Gosset lattice \cite{arxiv:math/0607446}.'
 
diff --git a/codes/classical/analog/sphere_packing/lattice/dual/leech.yml b/codes/classical/analog/sphere_packing/lattice/dual/leech.yml
@@ -34,17 +34,19 @@ relations:
     - code_id: hexagonal
       detail: 'The \(A_2\) hexagonal lattice can be specified as a section of the Leech lattice \cite[Fig. 6.2]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: dthree
-      detail: 'The \(D_3\) lattice can be specified as a section of the Leech lattice \cite[Fig. 6.2]{doi:10.1007/978-1-4757-6568-7}.'
+      detail: 'The \(D_3\) lattice can be specified as a section of the Leech lattice \cite[Fig. 6.2]{doi:10.1007/978-1-4757-6568-7}. The Leech lattice can also be constructed via the Turyn construction and the holy construction using the octacode as the glue code; one of these constructions uses eight copies of the \(D_3\) fcc lattice \cite{doi:10.1109/18.391252,arxiv:math/0207208}.'
     - code_id: dfour
       detail: 'The \(D_4\) lattice can be specified as a section of the Leech lattice \cite[Fig. 6.2]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: esix
       detail: 'The \(E_6\) lattice can be specified as a section of the Leech lattice \cite[Fig. 6.2]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: eseven
       detail: 'The \(E_7\) lattice can be specified as a section of the Leech lattice \cite[Fig. 6.2]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: eeight
-      detail: 'The \(E_8\) lattice can be specified as a section of the Leech lattice \cite[Fig. 6.2]{doi:10.1007/978-1-4757-6568-7}.'
+      detail: 'The \(E_8\) lattice can be specified as a section of the Leech lattice \cite[Fig. 6.2]{doi:10.1007/978-1-4757-6568-7}. The Leech lattice admits a Turyn-type construction from two copies of the \(E_8\) lattice in the same space \cite[Ch. 8, pg. 211]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: extended_golay
       detail: 'Two copies of the 24-dimensional packing obtained from the extended Golay code can be fitted together without overlap to form the Leech lattice \cite[Ch. 5, pg. 145]{doi:10.1007/978-1-4757-6568-7}. Half of the lattice can be obtained using Construction \(B^{\star}\) \cite[Exam. 10.7.3]{preset:EricZin}.'
+    - code_id: combinatorial_design
+      detail: 'The Leech lattice is completely determined by the Steiner system \(S(5,8,24)\) formed by the octads of the extended Golay code \cite[Ch. 12, pg. 335, Thm. 6]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: golay
       detail: 'The Leech lattice can be obtained by lifting the Golay code to \(\mathbb{Z}_4\) \cite{doi:10.1109/18.312154}, appending a parity check, and applying \term{Construction \(A_4\)} \cite{doi:10.1007/3-540-57843-9_20} (see also \cite{doi:10.1098/rspa.1982.0071}).'
     - code_id: ternary_golay
@@ -53,8 +55,6 @@ relations:
       detail: 'Several spherical sharp configurations are derived from the Leech lattice \cite{arxiv:math/0607446}.'
     - code_id: octacode
       detail: 'The Leech lattice can be constructed via the Turyn construction and the holy construction using the octacode as the glue code; one of these constructions uses eight copies of the \(D_3\) fcc lattice \cite{doi:10.1109/18.391252,arxiv:math/0207208}.'
-    - code_id: dthree
-      detail: 'The Leech lattice can be constructed via the Turyn construction and the holy construction using the octacode as the glue code; one of these constructions uses eight copies of the \(D_3\) fcc lattice \cite{doi:10.1109/18.391252,arxiv:math/0207208}.'
     - code_id: modulation
       detail: 'Codewords of the Leech lattice have been proposed to be used for a modulation scheme \cite{doi:10.1109/49.29618}.'
     - code_id: pseudo_golay
diff --git a/codes/classical/analog/sphere_packing/lattice/dual/niemeier.yml b/codes/classical/analog/sphere_packing/lattice/dual/niemeier.yml
@@ -12,6 +12,8 @@ introduced: '\cite{doi:10.1016/0022-314X(73)90068-1}'
 
 description: |
   One of the 24 positive-definite even unimodular lattices of rank 24.
+  The 24 lattices are \(D_{24}\), \(D_{16}E_8\), \(E_8^3\), \(A_{24}\), \(D_{12}^2\), \(A_{17}E_7\), \(D_{10}E_7^2\), \(A_{15}D_9\), \(D_8^3\), \(A_{12}^2\), \(A_{11}D_7E_6\), \(E_6^4\), \(A_9^2D_6\), \(D_6^4\), \(A_8^3\), \(A_7^2D_5^2\), \(A_6^4\), \(A_5^4D_4\), \(D_4^6\), \(A_4^6\), \(A_3^8\), \(A_2^{12}\), \(A_1^{24}\), and the Leech lattice \cite[Table 16.1]{doi:10.1007/978-1-4757-6568-7}.
+
 
 relations:
   parents:
@@ -24,6 +26,14 @@ relations:
       detail: 'The nine inequivalent \([24,12]\) doubly even self-dual codes \cite{doi:10.1016/0097-3165(75)90042-4} yield certain Niemeier lattices via \term{Construction A} \cite{doi:10.1006/eujc.1999.0360}. Niemeier lattices can be constructed from ternary self-dual codes of length 24 \cite{doi:10.1016/0012-365X(93)E0088-L}.'
     - code_id: self_dual_over_zq
       detail: 'Extremal Type II self-dual codes of length 24 over \(\mathbb{Z}_6\) yield Niemeier lattices \cite{doi:10.1006/eujc.2002.0557}.'
+    - code_id: tetracode
+      detail: 'The tetracode is the glue code for the Niemeier lattice \(E_6^4\) \cite[Ch. 16, pg. 408]{doi:10.1007/978-1-4757-6568-7}.'
+    - code_id: hexacode
+      detail: 'The hexacode is the glue code for the Niemeier lattice \(D_4^6\) \cite[Ch. 16, pg. 408]{doi:10.1007/978-1-4757-6568-7}.'
+    - code_id: ternary_golay
+      detail: 'The extended ternary Golay code is the glue code for the Niemeier lattice \(A^{12}_2\) \cite[Ch. 16, pg. 408]{doi:10.1007/978-1-4757-6568-7}.'
+    - code_id: extended_golay
+      detail: 'The extended Golay code is the glue code for the Niemeier lattice \(A_1^{24}\) \cite[Ch. 16, pg. 408]{doi:10.1007/978-1-4757-6568-7}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/classical/analog/sphere_packing/lattice/root/dn/dfour.yml b/codes/classical/analog/sphere_packing/lattice/root/dn/dfour.yml
@@ -28,6 +28,10 @@ relations:
   cousins:
     - code_id: parity_check
       detail: 'The \(D_4\) lattice is constructed out of the \([4,3,2]\) SPC codes via \term{Construction A} \cite[pg. 138]{doi:10.1007/978-1-4757-6568-7}.'
+    - code_id: repetition
+      detail: 'Construction \(A_c\) applied to the binary repetition code \(\{00,11\}\) over the Gaussian integers yields a Gaussian lattice whose corresponding real lattice is \(D_4\) \cite[Ch. 7, pg. 202]{doi:10.1007/978-1-4757-6568-7}.'
+    - code_id: 24cell
+      detail: 'The Voronoi cell of the \(D_4\) lattice is a 24-cell \cite[Ch. 21, pg. 464]{doi:10.1007/978-1-4757-6568-7}.'
     # - code_id: parity_check
     #   detail: 'The \([4,3,2]\) SPC code yields the \(D_4\) hyper-diamond lattice via \term{Construction A}.'
 
diff --git a/codes/classical/analog/sphere_packing/lattice/root/dn/dthree.yml b/codes/classical/analog/sphere_packing/lattice/root/dn/dthree.yml
@@ -29,6 +29,9 @@ relations:
       detail: 'The \(D_3\) root lattice is equivalent to the \(A_3\) root lattice \cite[Ch. 10]{preset:EricZin}.'
     - code_id: an
       detail: 'The \(D_3\) fcc lattice is equivalent to the \(A_3\) root lattice \cite[Ch. 1, pg. 13]{doi:10.1007/978-1-4757-6568-7}.'
+  cousins:
+    - code_id: rhombic_dodecahedron
+      detail: 'The Voronoi cell of the \(D_3\) fcc lattice is a rhombic dodecahedron \cite[Ch. 21, pg. 464]{doi:10.1007/978-1-4757-6568-7}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/classical/analog/sphere_packing/lattice/root/eseven.yml b/codes/classical/analog/sphere_packing/lattice/root/eseven.yml
@@ -12,7 +12,7 @@ short_name: '\(E_7\)'
 #introduced: '\cite{manual:{Gosset, Thorold. "On the regular and semi-regular figures in space of n dimensions." Messenger of Mathematics 29 (1900): 43-48.}}'
 
 description: |
-  Lattice in dimension \(7\).
+  Exceptional root lattice in dimension \(7\).
 
   A generating matrix for the lattice embedded in eight dimensions is \cite{doi:10.1007/978-1-4757-6568-7}
   \begin{align}
@@ -27,6 +27,8 @@ description: |
   \end{bmatrix}~.
   \end{align}
 
+  The Voronoi cell of the lattice is the reciprocal of the Gosset \(2_{31}\) polytope \cite[Ch. 21, pg. 465]{doi:10.1007/978-1-4757-6568-7}.
+
 protection: 'The \(E_7\) root lattice exhibits the densest lattice packing \cite{manual:{Blichfeldt, H. F. "On the minimum value of positive real quadratic forms in 6 variables." Bulletin of American Math. Soc 31 (1925): 386.},doi:10.1007/BF01454863,doi:10.1007/BF01201341,doi:10.1112/plms/s3-13.1.549,manual:{Vetchinkin, N. M. "Uniqueness of classes of positive quadratic and highest known kissing number in seven dimensions."}}.'
 
 
diff --git a/codes/classical/analog/sphere_packing/lattice/root/esix.yml b/codes/classical/analog/sphere_packing/lattice/root/esix.yml
@@ -12,7 +12,7 @@ short_name: '\(E_6\)'
 #introduced: '\cite{manual:{Gosset, Thorold. "On the regular and semi-regular figures in space of n dimensions." Messenger of Mathematics 29 (1900): 43-48.}}'
 
 description: |
-  Lattice in dimension \(6\).
+  Exceptional root lattice in dimension \(6\).
 
   A generating matrix for the lattice embedded in eight dimensions is \cite{doi:10.1007/978-1-4757-6568-7}
   \begin{align}
@@ -34,7 +34,9 @@ relations:
     - code_id: root
   cousins:
     - code_id: q-ary_repetition
-      detail: 'The \([3,1,3]_3\) ternary repetition code can be used to obtain the \(E_6\) root lattice \cite[Exam. 10.5.4]{preset:EricZin}.'
+      detail: 'The \([3,1,3]_3\) ternary repetition code can be used to obtain the \(E_6\) root lattice \cite[Exam. 10.5.4]{preset:EricZin}\cite[Ch. 7, pg. 200]{doi:10.1007/978-1-4757-6568-7}.'
+    - code_id: rect_hessian_polyhedron
+      detail: 'The Voronoi cell of the \(E_6\) root lattice is the dual of the Gosset \(1_{22}\) polytope \cite[Ch. 21, pg. 465]{doi:10.1007/978-1-4757-6568-7}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/classical/bits/constant_weight/combinatorial_design.yml b/codes/classical/bits/constant_weight/combinatorial_design.yml
@@ -62,11 +62,11 @@ relations:
     - code_id: pless_symmetry
       detail: 'The supports of fixed-weight codewords of certain Pless symmetry codes support combinatorial designs \cite{doi:10.1111/j.1749-6632.1970.tb56485.x,doi:10.1016/0097-3165(72)90088-X,arxiv:0811.1254}.'
     - code_id: golay
-      detail: 'The supports of the weight-seven codewords of the Golay code support the Steiner system \(S(4,7,23)\) \cite{doi:10.4153/CJM-1957-003-8,arxiv:0811.1254}\cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}. Its blocks are called octads.'
+      detail: 'The supports of the weight-seven codewords of the Golay code support the Steiner system \(S(4,7,23)\) \cite{doi:10.4153/CJM-1957-003-8,arxiv:0811.1254}\cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}.'
     - code_id: extended_golay
-      detail: 'The supports of the weight-eight codewords of the extended Golay code support the Steiner system \(S(5,6,12)\) \cite{doi:10.4153/CJM-1957-003-8,arxiv:0811.1254}\cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}. Its blocks are called octads.'
+      detail: 'The supports of the weight-eight codewords of the extended Golay code support the Steiner system \(S(5,8,24)\) \cite{doi:10.4153/CJM-1957-003-8,arxiv:0811.1254}\cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}\cite[Ch. 10, pg. 276]{doi:10.1007/978-1-4757-6568-7}. Its blocks are called octads.'
     - code_id: ternary_golay
-      detail: 'The supports of the weight-five (weight-six) codewords of the (extended) ternary Golay code support the Steiner system \(S(4,5,11)\) (\(S(5,6,12)\)) \cite{doi:10.4153/CJM-1957-003-8,arxiv:0811.1254}\cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}. Its blocks are called hexads.'
+      detail: 'The supports of the weight-five codewords of the ternary Golay code and the weight-six codewords of the extended ternary Golay code support the Steiner systems \(S(4,5,11)\) and \(S(5,6,12)\), respectively \cite{doi:10.4153/CJM-1957-003-8,arxiv:0811.1254}\cite[pg. 89]{doi:10.1007/978-1-4757-6568-7}. The latter blocks are called hexads.'
     - code_id: perfect
       detail: 'Perfect codes and combinatorial designs are related \cite{doi:10.1137/1016056,doi:10.1016/S1571-0653(04)00398-1}.'
     - code_id: dual
diff --git a/codes/classical/q-ary_digits/easy/tetracode.yml b/codes/classical/q-ary_digits/easy/tetracode.yml
@@ -44,7 +44,7 @@ relations:
       detail: 'Extended ternary Golay codewords can be obtained from tetracodewords \cite{doi:10.1007/978-1-4757-6568-7}.
       The tetracode can be used to decode the extended ternary Golay code \cite{doi:10.1109/TIT.1986.1057197}.'
     - code_id: eeight
-      detail: 'The \([4,2,3]_3\) tetracode can be used to obtain the \(E_8\) Gosset lattice \cite[Exam. 10.5.5]{preset:EricZin}.'
+      detail: 'The \([4,2,3]_3\) tetracode can be used to obtain the \(E_8\) Gosset lattice \cite[Exam. 10.5.5]{preset:EricZin}\cite[Ch. 7, pg. 200]{doi:10.1007/978-1-4757-6568-7}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/classical/spherical/polytope/4d/600cell/600cell.yml b/codes/classical/spherical/polytope/4d/600cell/600cell.yml
@@ -10,10 +10,13 @@ logical: reals
 name: '600-cell code'
 introduced: '\cite{doi:10.1007/978-3-0348-4117-7_8}'
 
+alternative_names:
+  - 'Hexacosichoron code'
+
 description: |
   Spherical \((4,120,(3-\sqrt{5})/2)\) code whose codewords are the vertices of the 600-cell.
   See \cite[Table 1]{arxiv:0911.2289}\cite[Table 3]{doi:10.3390/sym2031423} for realizations of the 120 codewords.
-  A realization in terms of icosians, which are quaternion coordinates of the 120 elements of the binary icosahedral group \(2I\) \cite{arxiv:2205.04965}.
+  A realization of the 600-cell can be done in terms of icosians, which are quaternion coordinates of the 120 elements of the binary icosahedral group \(2I \cong 2.A_5\) (a.k.a. icosian group) \cite[Ch. 8, pg. 207]{doi:10.1007/978-1-4757-6568-7}\cite{arxiv:2205.04965}.
 
   \begin{figure}
     \includegraphics{600cell.svg}
@@ -42,7 +45,9 @@ relations:
     - code_id: 120cell
       detail: 'Vertices of a 120-cell can be split up into vertices of five 600-cells \cite{preset:coxeter,arxiv:1309.7530}. The 600-cell and 120-cell are dual to each other.'
     - code_id: icosahedron
-      detail: 'A realization of the 600-cell in terms of quaternion coordinates yields the 120 elements of the binary icosahedral group \(2I\) \cite{arxiv:2205.04965}.'
+      detail: 'A realization of the 600-cell can be done in terms of icosians, which are quaternion coordinates of the 120 elements of the binary icosahedral group \(2I \cong 2.A_5\) (a.k.a. icosian group) \cite[Ch. 8, pg. 207]{doi:10.1007/978-1-4757-6568-7}\cite{arxiv:2205.04965}.'
+    - code_id: witting_polytope
+      detail: 'The 120 vertices of the 600-cell are the unit icosians, and these icosian units, together with their multiples by \((1-\sqrt{5})/2\), form the 240 minimal vectors of a version of the \(E_8\) lattice, i.e., the Witting polytope \cite[Ch. 8, pg. 210]{doi:10.1007/978-1-4757-6568-7}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/classical/spherical/polytope/6-8d/8d/witting_polytope.yml b/codes/classical/spherical/polytope/6-8d/8d/witting_polytope.yml
@@ -32,9 +32,9 @@ notes:
 relations:
   parents:
     - code_id: self_dual_polytope
-      detail: 'The Witting polytope is self-dual.'
+      detail: 'The Witting polytope is self-dual as a complex polytope. The \(4_{21}\) real polytope is not self-dual \cite{preset:coxeter}.'
     - code_id: eeight_shell
-      detail: 'The minimal shell of the lattice yields the \((8,240,1)\) code, whose codewords form the vertices of the \(4_{21}\) real polytope and the Witting complex polytope.'
+      detail: 'The minimal shell of the lattice yields the \((8,240,1)\) code, whose codewords form the vertices of the \(4_{21}\) real polytope.'
     #  Also in eeight_shell
     - code_id: sharp_config
       detail: 'The Witting polytope code is a sharp configuration \cite{doi:10.1515/dma.1994.4.2.143,arxiv:math/0607446}.'
diff --git a/codes/classical/spherical/polytope/6-8d/hess_polytope.yml b/codes/classical/spherical/polytope/6-8d/hess_polytope.yml
@@ -38,7 +38,7 @@ relations:
     - code_id: complex_projective
       detail: 'Antipodal pairs of points of the \(3_{21}\) polytope code correspond to the 28 bitangent lines of a general quartic plane curve in the complex project plane \cite{doi:10.1112/plms/s2-35.1.23,manual:{Arnold, V. I. (1999). Symplectization, complexification and mathematical trinities. The Arnoldfest, 23-37.},arxiv:math/0607446,arxiv:1505.06742}.'
     - code_id: witting_polytope
-      detail: '\(3_{21}\) polytope codewords form the kissing configuration of the Witting polytope code; see Ref. \cite{arxiv:math/0607446}. The Gosset graph is a subgraph of the graph formed by the vertices of the Witting polytope \cite[Sec. 3.11]{doi:10.1007/978-3-642-74341-2}.'
+      detail: '\(3_{21}\) polytope codewords form the kissing configuration of the Witting polytope code \cite[Ch. 9, pg. 264]{doi:10.1007/978-1-4757-6568-7}\cite{arxiv:math/0607446}. The Gosset graph is a subgraph of the graph formed by the vertices of the Witting polytope \cite[Sec. 3.11]{doi:10.1007/978-3-642-74341-2}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/classical/spherical/polytope/dual_polytope.yml b/codes/classical/spherical/polytope/dual_polytope.yml
@@ -9,6 +9,9 @@ logical: reals
 
 name: 'Dual polytope code'
 
+alternative_names:
+  - 'Reciprocal polytope code'
+
 description: |
   For a spherical code whose codewords are vertices of a convex polytope, the dual code consists of codewords corresponding to the facets of the polar dual polytope. For regular polytopes, these dual codewords can be represented by the normalized centers of the facets of the original polytope. The dual codewords make up the vertices of the polytope dual to the original polytope.
 
diff --git a/codes/classical/spherical/polytope/self_dual_polytope.yml b/codes/classical/spherical/polytope/self_dual_polytope.yml
@@ -9,6 +9,9 @@ logical: reals
 
 name: 'Self-dual polytope code'
 
+alternative_names:
+  - 'Self-reciprocal polytope code'
+
 description: |
   A spherical code whose codewords are the vertices of a self-dual polytope.
 
diff --git a/codes/quantum/qubits/dynamic/spacetime_circuit.yml b/codes/quantum/qubits/dynamic/spacetime_circuit.yml
@@ -30,6 +30,8 @@ description: |
 features:
   decoders:
     - 'Efficient decoders can be constructed for some circuits \cite{arxiv:2304.05943}.'
+  fault_tolerance:
+    - 'The outcome-code distance is a lower bound on the \hyperref[topic:effective-distance]{circuit-level distance}, and the bound need not be tight because some undetectable fault configurations are logically trivial. The circuit-level distance corresponds to the minimum-weight outcome codeword that is not in the kernel of the logical effect matrix \cite{arxiv:2401.12017}.'
 
 relations:
   parents:
@@ -56,5 +58,11 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: MarcusPS
+      date: '2026-03-18'
+    - user_id: DavidAasen
+      date: '2026-03-18'
+    - user_id: VictorVAlbert
+      date: '2026-03-18'
     - user_id: VictorVAlbert
       date: '2023-05-11'
diff --git a/codes/quantum/qubits/qubits_into_qubits.yml b/codes/quantum/qubits/qubits_into_qubits.yml
diff --git a/codes/quantum/qubits/stabilizer/qubit_css.yml b/codes/quantum/qubits/stabilizer/qubit_css.yml
