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\(BW_{32}\) lattice-shell code

Description

Spherical code whose codewords are points on the \(BW_{32}\) Barnes-Wall lattice normalized to lie on the unit sphere.

The minimal shell of the lattice yields the \((32,146880,1)\) code.

Cousin

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Primary Hierarchy

Classical Domain
Spherical Kingdom
Constant-energy codeECC
Spherical code
Lattice-shell code
Parents
Lattice-shell code
Real-Clifford subgroup-orbit codeSpherical design \(t\)-design ECC
The minimal \(BW_{32}\) lattice-shell code is equivalent to the real Clifford subgroup-orbit code for \(n=32\).
\(BW_{32}\) lattice-shell code
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Cite as:

“\(BW_{32}\) lattice-shell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/bw32_shell

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/lattice_shell/bw32_shell.yml.