Description
Spherical code whose codewords are the vertices of a polytope, i.e., a geometrical figure bounded by lines, planes, and hyperplanes [1]. Polytopes in two (three) real or complex dimensions are called polygons (polyhedra).
Notes
See Polytope Wiki and webpage by R. Klitzing for lists of polytopes.
Parent
- Slepian group-orbit code — Vertices of polytope codes typically form an orbit of the polytope's symmetry group.
Children
- 120-cell code
- Cubeoctahedron code
- \(3_{21}\) polytope code
- Hessian polyhedron code
- Rectified Hessian polyhedron code
- Icosahedron code
- Biorthogonal spherical code — Biorthogonal spherical codewords in 2 (3, 4, \(n\)) dimensions form the vertices of a square (octahedron, 16-cell, \(n\)-orthoplex).
- Hypercube code — Hypercube codewords in 2 (3, 4, \(n\)) dimensions form the vertices of a triangle (sqaure, cube, \(n\)-cube).
- Simplex spherical code — Simplex spherical codewords in 2 (3, 4, \(n\)) dimensions form the vertices of a triangle (tetrahedron, 5-cell, \(n\)-simplex).
- Polygon code
- Snub-cube code
- Square-antiprism code
- Witting polytope code
Cousins
- Ball color code — Polytopes dual to the hyperoctahedron, truncated octahedron, truncated cuboctahedron, and truncated icosidodecahedron are used to construct 3D ball color codes.
- \([[30,8,3]]\) Bring code — Bring code and related codes listed in [2; Table 1] arrange qubits and stabilizer generators on polytopes.
- Rhombic dodecahedron surface code — The rhombic dodecahedron surface code arranges qubits and stabilizer generators on polytopes.
References
- [1]
- H. S. M. Coxeter. Regular polytopes. Courier Corporation, 1973.
- [2]
- J. Conrad et al., “The small stellated dodecahedron code and friends”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, 20170323 (2018) arXiv:1712.07666 DOI
Page edit log
- Victor V. Albert (2022-11-16) — most recent
Cite as:
“Polytope code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/polytope