dodecahedron + links to it

codes/classical/bits/cyclic/golay.yml

@@ -99,6 +99,10 @@ relations:
       detail: 'The dual of the Golay code forms a spherical three-design under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite[Exam. 9.3]{doi:10.1007/BF03187604}.'
     - code_id: lexicographic
       detail: 'The extended Golay code is a lexicode \cite{manual:{M. J. T. Guy, unpublished.},doi:10.1109/TIT.1986.1057187}\cite[pg. 327]{preset:MacSlo}.'
+    - code_id: icosahedron
+      detail: 'The parity bits of the extended Golay code can be visualized to lie on the vertices of the icosahedron; see \href{https://blogs.ams.org/visualinsight/2015/12/01/golay-code/}{post} by J. Baez for more details. To construct the Golay code, one can use the great dodecahedron to generate codewords by placing message bits on the faces and calculating the parity bits that live on the 12 vertices of the inner icosahedron.'
+    - code_id: dodecahedron
+      detail: 'The parity bits of the extended Golay code can be visualized to lie on the vertices of the icosahedron; see \href{https://blogs.ams.org/visualinsight/2015/12/01/golay-code/}{post} by J. Baez for more details. To construct the Golay code, one can use the great dodecahedron to generate codewords by placing message bits on the faces and calculating the parity bits that live on the 12 vertices of the inner icosahedron.'
 
 
 # The Golay code can be constructed as a cyclic code with the generator polynomial \(x^{11} + x^{10} + x^6 + x^5 + x^4 + x^2 + 1\) over \(GF(2)\).

codes/classical/bits/graph/incidence/petersen.yml

@@ -21,6 +21,9 @@ relations:
   parents:
     - code_id: homological_classical
     - code_id: small_distance
+  cousins:
+    - code_id: dodecahedron
+      detail: 'The Petersen graph can be thought of as a dodecahedron with antipodes identified \cite[Appx. A.2.1]{arxiv:1703.07847}.'
 
 
 # Begin Entry Meta Information

codes/classical/q-ary_digits/ag/reed_solomon/berlekamp.yml

@@ -24,7 +24,7 @@ relations:
     - code_id: alternant
       detail: 'Berlekamp codes reduce to narrow-sense alternant codes for \(p=2\) \cite[Ch. 10.6]{doi:10.1017/CBO9780511808968}.'
     - code_id: reed_solomon
-      detail: 'Berlekamp codes are obtained by first constructing an RS-like parity-check matrix out of a certain \hyperref[topic:finite-fields]{field extension} of \(GF(p)\) and then taking the \hyperref[topic:finite-fields]{subfield} subcode of the corresponding code; see \cite[Ch. 10.6]{doi:10.1017/CBO9780511808968}..'
+      detail: 'Berlekamp codes are obtained by first constructing an RS-like parity-check matrix out of a certain \hyperref[topic:finite-fields]{field extension} of \(GF(p)\) and then taking the \hyperref[topic:finite-fields]{subfield} subcode of the corresponding code; see \cite[Ch. 10.6]{doi:10.1017/CBO9780511808968}.'
 
 
 # Begin Entry Meta Information

codes/classical/spherical/polytope/dodecahedron.yml

@@ -0,0 +1,33 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: dodecahedron
+physical: spheres
+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).
+
+
+relations:
+  parents:
+    - code_id: polytope
+    - code_id: spherical_design
+      detail: 'The dodecahedron code forms a spherical 5-design \cite{arxiv:2302.11593}.'
+  cousins:
+    - code_id: dual_polytope
+      detail: 'The icosahedron and dodecahedron are dual to each other.'
+    - code_id: icosahedron
+      detail: 'The icosahedron and dodecahedron are dual to each other.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-12-10'

codes/classical/spherical/polytope/icosahedron.yml

@@ -26,8 +26,6 @@ relations:
     - code_id: spherical_design
       detail: 'The icosahedron code forms a unique tight spherical 5-design \cite{doi:10.1007/BF03187604}\cite[Exam. 9.6.1]{preset:EricZin}.'
   cousins:
-    - code_id: golay
-      detail: 'The parity bits of the extended Golay code can be visualized to lie on the vertices of the icosahedron; see \href{https://blogs.ams.org/visualinsight/2015/12/01/golay-code/}{post} by J. Baez for more details.'
     - code_id: dual_polytope
       detail: 'The icosahedron and dodecahedron are dual to each other.'
 

codes/classical/spherical/polytope/infinite/simplex_spherical.yml

@@ -29,7 +29,7 @@ relations:
       detail: 'Simplex spherical codes are the only tight spherical 2-designs \cite[Tab. 9.3]{preset:EricZin}.'
     - code_id: permutation_spherical
   cousins:
-    - code_id: icosahedron
+    - code_id: dodecahedron
       detail: 'Vertices of a dodecahedron can be split up into vertices of five tetrahedra, which are simplex spherical codes for \(n=3\) \cite{preset:coxeter}.'
     - code_id: binary_antipodal
       detail: 'Binary simplex codes map to \((2^m,2^m+1)\) simplex spherical codes under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite[Sec. 6.5.2]{manual:{Forney, G. D. (2003). 6.451 Principles of Digital Communication II, Spring 2003.}}\cite[pg. 18]{preset:EricZin}. In other words, simplex (simplex spherical) codes form simplices in Hamming (Euclidean) space.'

codes/classical/spherical/polytope/pentakis_dodecahedron.yml

@@ -21,6 +21,8 @@ relations:
   cousins:
     - code_id: icosahedron
       detail: 'The pentakis dodecahedron is the convex hull of the icosahedron and dodecahedron.'
+    - code_id: dodecahedron
+      detail: 'The pentakis dodecahedron is the convex hull of the icosahedron and dodecahedron.'
 
 
 # Begin Entry Meta Information

codes/quantum/oscillators/stabilizer/lattice/multimodegkp.yml

@@ -22,7 +22,10 @@ description: |
 protection: 'The level of protection against displacement errors is quantified by the Euclidean code distance \(\Delta=\min_{x\in {\mathcal{L}}^{\perp}\setminus {\mathcal{L}}} \|x\|_2\) \cite{arxiv:2109.14645}.'
 
 features:
-  rate: 'Transmission schemes with multimode GKP codes achieve, up to a constant-factor offset, the capacity of \hyperref[topic:ad]{AD}, a lower bound on displacement-noise, and a lower bound on thermal-noise Gaussian channel capacities \cite{arxiv:quant-ph/0105058,arxiv:1708.07257,arxiv:1801.04731,arxiv:1801.07271}. Particular random lattice families of multimode GKP codes achieve the hashing bound of the displacement noise channel \cite{arxiv:quant-ph/0105058}.'
+  rate: |
+    Transmission schemes with multimode GKP codes achieve a lower bound on displacement noise and a lower bound on the thermal-noise Gaussian channel capacities \cite{arxiv:quant-ph/0105058,arxiv:1708.07257,arxiv:1801.04731,arxiv:1801.07271}. 
+    Particular random lattice families of multimode GKP codes achieve the hashing bound of the displacement noise channel \cite{arxiv:quant-ph/0105058}.
+    Particular families of GKP codes achieve the capacity of \hyperref[topic:ad]{AD} and amplifications channels \cite{arxiv:2412.06715}.
 
   encoders:
     - 'GKP codes with fixed \(n\) and prime-dimensional logical Hilbert space are symplectically related to a disjoint product of single-mode GKP codes on \(n\) modes, such that encoding via Gaussian unitaries is possible.'

codes/quantum/qubits/small_distance/small/quantum_dodecahedron.yml

@@ -11,7 +11,7 @@ name: '\([[16,4,3]]\) dodecahedral code'
 introduced: '\cite{arxiv:2411.14448}'
 
 description: |
-  A \([[16,4,3]]\) qubit stabilizer code defined whose \hyperref[topic:encoder-respecting]{encoder-respecting form} is the graph of vertices of a dodecahedron \cite{arxiv:2411.14448}..
+  A \([[16,4,3]]\) qubit stabilizer code defined whose \hyperref[topic:encoder-respecting]{encoder-respecting form} is the graph of vertices of a dodecahedron \cite{arxiv:2411.14448}.
 
 features:
   rate: 'The code has a rate of \(1/4\), higher than that of the five-qubit perfect code.'
@@ -23,6 +23,9 @@ relations:
   parents:
     - code_id: qubit_stabilizer
     - code_id: small_distance_quantum
+  cousins:
+    - code_id: dodecahedron
+      detail: 'The \hyperref[topic:encoder-respecting]{encoder-respecting form} of the \([[16,4,3]]\) dodecahedral code is the graph of vertices of a dodecahedron \cite{arxiv:2411.14448}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/topological/surface/2d_surface/stellated_dodecahedron_css.yml

@@ -29,7 +29,9 @@ relations:
     - code_id: polytope
       detail: 'Bring code and related codes listed in \cite[Table 1]{arxiv:1712.07666} arrange qubits and stabilizer generators on star polyhedra.'
     - code_id: golay
-      detail: 'The automorphism group of the parity-check matrix of the Golay code is the same as a certai automorphism group of the Bring code \cite{arxiv:2202.06647}.'
+      detail: 'The automorphism group of the parity-check matrix of the Golay code is the same as a certain automorphism group of the Bring code \cite{arxiv:2202.06647}.'
+    - code_id: dodecahedron
+      detail: 'The qubits and stabilizer generators of the \([[30,8,3]]\) Bring code lie on the vertices of the small stellated dodecahedron.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/stabilizer/topological/surface/non-css/rhombic_dodecahedron_surface.yml

@@ -7,7 +7,7 @@ code_id: rhombic_dodecahedron_surface
 physical: qubits
 logical: qubits
 
-name: 'Rhombic dodecahedron surface code'
+name: '\([[14,3,3]]\) Rhombic dodecahedron surface code'
 introduced: '\cite{arxiv:2010.06628}'
 
 alternative_names:
@@ -25,6 +25,8 @@ relations:
   cousins:
     - code_id: polytope
       detail: 'The rhombic dodecahedron surface code arranges qubits and stabilizer generators on polytopes.'
+    - code_id: dodecahedron
+      detail: 'The qubits of the \([[14,3,3]]\) rhombic dodecahedron surface code lie on the vertices of the small stellated dodecahedron.'
 
 
 # Begin Entry Meta Information