Description
Spherical code whose codewords are points on the \(E_7\) lattice normalized to lie on the unit sphere.Cousins
- \(E_7\) root lattice— The \(E_7\) lattice-shell code is obtained from a shell of the \(E_7\) lattice.
- \(3_{21}\) polytope code— \(3_{21}\) polytope codewords form the minimal lattice-shell code of the \(E_7^{\perp}\) lattice [1].
Member of code lists
Primary Hierarchy
Parents
\(E_7\) lattice-shell code
Children
Codewords of the \(2_{31}\) polytope form the smallest shell of the \(E_7\) lattice [2].
References
- [1]
- J. H. Conway and N. J. A. Sloane, “The Cell Structures of Certain Lattices”, Miscellanea Mathematica 71 (1991) DOI
- [2]
- S. Borodachov, “Odd strength spherical designs attaining the Fazekas–Levenshtein bound for covering and universal minima of potentials”, Aequationes mathematicae 98, 509 (2024) DOI
Page edit log
- Victor V. Albert (2022-03-05) — most recent
Cite as:
“\(E_7\) lattice-shell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/eseven_shell