[Jump to code hierarchy]

Polygon code

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 (\(q=6\)).

Figure I: \(q\)-gon code for \(q=5\). Each codeword is a vertex of the \(5\)-gon.

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.
Page edit log

Cite as:

“Polygon code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/polygon

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/polytope/2d/polygon.yml.