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\(\Lambda_{16}\) lattice-shell code

Description

Spherical code whose codewords are points on the \(\Lambda_{16}\) Barnes-Wall lattice normalized to lie on the unit sphere.

The minimal shell of the lattice yields the \((16,4320,1)\) code.

Cousin

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Primary Hierarchy

Classical Domain
Spherical Kingdom
Constant-energy spherical codeECC
Spherical code
Lattice-shell code
Parents
Lattice-shell code
Real-Clifford subgroup-orbit codeSpherical design ECC \(t\)-design
The minimal \(\Lambda_{16}\) lattice-shell code is equivalent to the real Clifford subgroup-orbit code for \(n=16\).
\(\Lambda_{16}\) lattice-shell code
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Zoo Code ID: lambda16_shell

Cite as:
“\(\Lambda_{16}\) lattice-shell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/lambda16_shell, arXiv:2606.11484
BibTeX:
@incollection{eczoo_lambda16_shell,
title={\(\Lambda_{16}\) 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/lambda16_shell}
}
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Permanent link:
https://errorcorrectionzoo.org/c/lambda16_shell

Cite as:

“\(\Lambda_{16}\) lattice-shell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/lambda16_shell, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/lattice_shell/lambda16_shell.yml.