Petersen spherical code[1]
Description
A \((4,10,1/6)\) spherical code whose codewords correspond to vertices of the Peterson graph. Its Gram matrix is constructed by putting \(-2/3\) whenever two vertices are adjacent in the graph, and \(1/6\) otherwise. The code is optimal for its parameters [1].
Parent
- Spherical design — The Peterson spherical code forms a spherical two-design [1].
Cousins
- Petersen cycle code
- Simplex spherical code — Codewords of the Petersen spherical code correspond to midpoints of the \(5\)-cell [1].
References
- [1]
- C. Bachoc and F. Vallentin, “Optimality and uniqueness of the (4,10,1/6) spherical code”, Journal of Combinatorial Theory, Series A 116, 195 (2009) arXiv:0708.3947 DOI
Page edit log
- Victor V. Albert (2024-04-20) — most recent
Cite as:
“Petersen spherical code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/petersen_spherical