\(E_6\) lattice-shell code 

Description

Spherical code whose codewords are points on the \(E_6\) lattice normalized to lie on the unit sphere.

The minimal shell of the lattice yields the \((6,72,1)\) code, whose codewords form the vertices of the \(1_{22}\) real polytope and the rectified Hessian polyhedron.

Parent

Child

Cousins

References

[1]
H. Cohn and A. Kumar, “Universally optimal distribution of points on spheres”, Journal of the American Mathematical Society 20, 99 (2006) arXiv:math/0607446 DOI
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Zoo Code ID: esix_shell

Cite as:
“\(E_6\) lattice-shell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/esix_shell
BibTeX:
@incollection{eczoo_esix_shell,
  title={\(E_6\) lattice-shell code},
  booktitle={The Error Correction Zoo},
  year={2022},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/esix_shell}
}
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Permanent link:
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Cite as:

“\(E_6\) lattice-shell code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/esix_shell

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/spherical/lattice_shell/esix_shell.yml.