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codes/classical/bits/reed_muller/biorthogonal.yml

@@ -42,6 +42,8 @@ relations:
     - code_id: biorthogonal_spherical
       detail: 'Each first-order RM code maps to a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{manual:{Forney, G. D. (2003). 6.451 Principles of Digital Communication II, Spring 2003.}}\cite[pg. 19]{preset:EricZin}.
       In other words, first-order RM (biorthogonal spherical) codes form orthoplexes in Hamming (Euclidean) space.'
+    - code_id: dual_polytope
+      detail: 'Orthoplexes and hypercubes are dual to each other.'
 
 
 # Begin Entry Meta Information

codes/classical/spherical/polytope/polychoron/120cell.yml

@@ -22,6 +22,9 @@ relations:
     - code_id: polytope
     - code_id: spherical_design
       detail: 'The code forms a spherical 11-design because its vertices can be divided into five 600-cells, each of which forms said design.'
+  cousins:
+    - code_id: dual_polytope
+      detail: 'The 600-cell and 120-cell are dual to each other.'
 
 
 # Begin Entry Meta Information

codes/classical/spherical/polytope/polyhedron/dodecahedron.yml

@@ -10,7 +10,7 @@ logical: reals
 name: 'Dodecahedron code'
 
 description: |
-  Spherical \((3,20,2-2\sqrt{5}/2)\) code whose codewords are the vertices of the dodecahedron (alternatively, the centers of the faces of a icosahedron, the dodecahedron's dual polytope).
+  Spherical \((3,20,2-2\sqrt{5}/3)\) code whose codewords are the vertices of the dodecahedron (alternatively, the centers of the faces of a icosahedron, the dodecahedron's dual polytope).
 
 
 relations:

codes/classical/spherical/polytope/polytope.yml

@@ -11,7 +11,7 @@ name: 'Polytope code'
 
 description: |
   Spherical code whose codewords are the vertices of a polytope, i.e., a geometrical figure bounded by lines, planes, and hyperplanes \cite{preset:coxeter}.
-  Polytopes in two (three) real or complex dimensions are called polygons (polyhedra).
+  Polytopes in two (three, four) real or complex dimensions are called polygons (polyhedra, polychora).
 
 
 relations:

codes/classical_into_quantum/oscillators/coherent_state/psk/quantum_bpsk.yml

@@ -23,6 +23,7 @@ features:
     - 'Photon-number resolving detector \cite{arxiv:1807.05199}.'
     - 'Non-Gaussian near-optimal receiver \cite{arxiv:0706.1038}.'
     - 'Multi-stage quantum receiver \cite{arxiv:1404.5033}.'
+    - 'Quantum receiver attaining the Helstrom bound in the low-photon regime \cite{arxiv:2410.21800}.'
 
 realizations:
   - 'Linear-optical quantum receiver \cite{arxiv:1103.5592}.'