Description
An antipodal spherical \((7,126,1)\) code whose codewords are the vertices of the smallest shell of the \(E_7\) lattice [1].Notes
See the corresponding Bendwavy database entry [2].Cousins
- Sharp configuration— The 63 antipodal pairs of vertices of the \(2_{31}\) polytope form a sharp configuration in \(\mathbb{R}P^6\) [3].
- \(t\)-design— The 63 antipodal pairs of vertices of the \(2_{31}\) polytope form a 2-design in \(\mathbb{R}P^6\) [3].
- Real projective space code— The 63 antipodal pairs of vertices of the \(2_{31}\) polytope form a sharp configuration and a 2-design in \(\mathbb{R}P^6\) [3].
Member of code lists
Primary Hierarchy
References
- [1]
- S. Borodachov, “Odd strength spherical designs attaining the Fazekas–Levenshtein bound for covering and universal minima of potentials”, Aequationes mathematicae 98, 509 (2024) DOI
- [2]
- R. Klitzing. “Laq.” Polytopes & their Incidence Matrices. bendwavy.org/klitzing/incmats/laq.htm
- [3]
- H. Cohn and A. Kumar, “Universally optimal distribution of points on spheres”, Journal of the American Mathematical Society 20, 99 (2006) arXiv:math/0607446 DOI
- [4]
- B. Venkov. Réseaux et designs sphériques. In Réseaux euclidiens, designs sphériques et formes modulaires, volume 37 of Monogr. Enseign. Math., pages 10–86. Enseignement Math., Geneva, 2001
Page edit log
- Victor V. Albert (2026-04-20) — most recent
Cite as:
“\(2_{31}\) polytope code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/231_polytope