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.

Parents

Child

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.
  • \(A_2\) hexagonal lattice — The Voronoi cell of the hexagonal lattice is the hexagon.
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Zoo Code ID: polygon

Cite as:
“Polygon code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/polygon
BibTeX:
@incollection{eczoo_polygon, title={Polygon code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/polygon} }
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Permanent link:
https://errorcorrectionzoo.org/c/polygon

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.