\(D_4\) hyper-diamond lattice code

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

References

[1]
A. Korkine and G. Zolotareff, “Sur les formes quadratiques positives quaternaires”, Mathematische Annalen 5, 581 (1872) DOI
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Zoo Code ID: dfour

Cite as:
\(D_4\) hyper-diamond lattice code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/dfour
BibTeX:
@incollection{eczoo_dfour, title={\(D_4\) hyper-diamond lattice code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/dfour} }
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Cite as:

\(D_4\) hyper-diamond lattice code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/dfour

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/analog/lattice/root/dfour.yml.