\(D_3\) face-centered cubic (fcc) lattice code
Description
Laminated three-dimensional lattice consisting of layers of hexagonal lattices.
Protection
The \(D_3\) fcc lattice exhibits the densest lattice packing [1], highest kissing number of 12, and the thinnest lattice covering in three dimensions.
Parent
- \(D_n\) checkerboard lattice code — The \(D_3\) root lattice is equivalent to the \(A_3\) root lattice [2; Ch. 10].
Cousins
- Body-centered cubic (bcc) lattice code — The bcc and fcc lattices are dual to each other.
- Cubeoctahedron code — Cubeoctahedron codewords form the minimal shell of the \(D_3\) face-centered cubic (fcc) lattice.
References
- [1]
- C.F. Gauss, Besprechung des Buchs von L.A. Seeber, Untersuchungen uber die Eigenschaften der positiven terndren quadratischen Formen usw. Gottingsche Gelehrte Anzeigen, July 9, 1831 = Werke, II, pp. 188-196, 1876.
- [2]
- T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
Page edit log
- Victor V. Albert (2022-11-23) — most recent
Cite as:
“\(D_3\) face-centered cubic (fcc) lattice code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/dthree