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\(D_4\) lattice-shell code

Description

Spherical code whose codewords are points on the \(D_4\) lattice normalized to lie on the unit sphere.

Cousins

Member of code lists

Primary Hierarchy

Classical Domain
Spherical Kingdom
Constant-energy spherical codeECC
Spherical code
Lattice-shell code
Parents
Lattice-shell code
\(D_4\) lattice-shell code
Children
24-cell code
The 24-cell code is the minimal shell of the \(D_4\) lattice.
Disphenoidal 288-cell code
Disphenoidal 288-cell codewords are the union of two 24-point shells of the \(D_4\) lattice, with each shell making up the vertices of a 24-cell.

References

[1]
M. Hirao, H. Nozaki, and K. Tasaka, “Spherical designs and modular forms of the \(D_4\) lattice”, (2023) arXiv:2303.09000
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Zoo Code ID: dfour_shell

Cite as:
“\(D_4\) lattice-shell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/dfour_shell, arXiv:2606.11484
BibTeX:
@incollection{eczoo_dfour_shell,
title={\(D_4\) lattice-shell code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/dfour_shell}
}
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Permanent link:
https://errorcorrectionzoo.org/c/dfour_shell

Cite as:

“\(D_4\) lattice-shell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/dfour_shell, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/lattice_shell/dfour_shell.yml.