Description
Spherical \((1,q,4\sin^2 \frac{\pi}{q})\) code for any \(q\geq1\) whose codewords are the vertices of a \(q\)-gon. Special cases include the line segment (\(q=2\)), triangle (\(q=3\)), square (\(q=4\)), pentagon (\(q=5\)), and hexagon (\(q=6\)).
Cousins
- Cat code— The \(q(S+1)\)-component cat coherent-state constellation forms the vertices of a \(q(S+1)\)-gon.
- PSK c-q code— The PSK coherent-state constellation forms the vertices of a \(q\)-gon.
- Honeycomb tiling— The Voronoi cell of the honeycomb tiling is the triangle.
- \(A_2\) triangular lattice— The Voronoi cell of the triangular lattice is the hexagon.
Member of code lists
Primary Hierarchy
Parents
Polygons are self-dual.
Spherical sharp configurationSpherical design Sharp configuration \(t\)-design Universally optimal ECC
A \(q\)-gon is a tight spherical \(q-1\) design.
Polygon code
Children
The PSK constellation forms a \(q\)-gon.
Page edit log
- Shubham P. Jain (2023-02-27) — most recent
- Victor V. Albert (2023-02-24)
Cite as:
“Polygon code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/polygon