\(D_n\) checkerboard lattice code 

Description

Lattice code consisting of all points whose coordinates add up to an even integer. Its generator matrix can be represented by \begin{align} G=\begin{pmatrix}-1 & -1 & 0 & 0 & \cdots & 0 & 0\\ \phantom{-}1 & -1 & 0 & 0 & \cdots & 0 & 0\\ 0 & \phantom{-}1 & -1 & 0 & \cdots & 0 & 0\\ 0 & 0 & \phantom{-}1 & -1 & \cdots & 0 & 0\\ \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\ 0 & 0 & 0 & 0 & \cdots\phantom{-} & 1 & -1 \end{pmatrix}~. \tag*{(1)}\end{align}

Protection

Exhibits the densest lattice packing and highest known kissing number in four and five [1] dimensions.

Parent

Children

Cousin

References

[1]
Sur les formes quadratiques positives. (Zus. Mit S. Zolotareff) Korkine in: Mathematische Annalen
[2]
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
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Zoo Code ID: dn

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

\(D_n\) checkerboard lattice code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/dn

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