Description
Spherical code whose codewords are the vertices of a polytope, i.e., a geometrical figure bounded by lines, planes, and hyperplanes in either real [1] or complex [2] space. A polytope in two (three, four) dimensions is called a polygon (polyhedron, polychoron).Notes
See Polytope Wiki and webpage by R. Klitzing for lists of polytopes.Cousin
- Quantum spherical code (QSC)— QSCs can be constructed by using vertices of polytopes for logical constellations. The logical constellations form the vertices of the code constellation, a polytope compound.
Member of code lists
Primary Hierarchy
Parents
Vertices of polytope codes typically form an orbit of the polytope's symmetry group.
Polytope code
Children
Three-dimensional polytope codes are polyhedron codes.
Biorthogonal spherical codewords in 2 (3, 4, \(n\)) dimensions form the vertices of a square (octahedron, 16-cell, \(n\)-orthoplex).
Hypercube codewords in 2 (3, 4, \(n\)) dimensions form the vertices of a square (cube, tesseract, \(n\)-cube).
References
- [1]
- H. S. M. Coxeter. Regular polytopes. Courier Corporation, 1973.
- [2]
- H. S. M. Coxeter. Regular Complex Polytopes. Cambridge University Press, 1991.
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