Description
BW lattice in dimension \(4\), which is the lattice corresponding to the \([4,1,4]\) repetition and \([4,3,2]\) SPC codes via the mod-two lattice construction.
Protection
The \(D_4\) lattice has a density of \(\pi^2/16\approx 0.6169\) and nominal coding gain of \(\sqrt{2}\). It exhibits the densest lattice packing in four dimensions [1].
Parents
Cousins
- Repetition code — The four-bit repetition code yields the \(D_4\) hyper-diamond lattice code via the mod-two lattice construction.
- \(D_4\) lattice-shell code
- \(D_4\) hyper-diamond GKP code
References
- [1]
- A. Korkine and G. Zolotareff, “Sur les formes quadratiques positives quaternaires”, Mathematische Annalen 5, 581 (1872) DOI
Page edit log
- Victor V. Albert (2022-11-08) — most recent
Cite as:
“\(D_4\) hyper-diamond lattice code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/dfour