\(E_6\) root lattice code 

Description

Lattice in dimension \(6\).

Protection

The root \(E_6\) lattice exhibits the densest lattice packing [15] and highest known kissing number in six dimensions.

Parent

Cousins

References

[1]
Blichfeldt, H. F. "On the minimum value of positive real quadratic forms in 6 variables." Bulletin of American Math. Soc 31 (1925): 386.
[2]
H. F. Blichfeldt, “The minimum value of quadratic forms, and the closest packing of spheres”, Mathematische Annalen 101, 605 (1929) DOI
[3]
H. F. Blichfeldt, “The minimum values of positive quadratic forms in six, seven and eight variables”, Mathematische Zeitschrift 39, 1 (1935) DOI
[4]
G. L. Watson, “The Class-Number of a Positive Quadratic Form”, Proceedings of the London Mathematical Society s3-13, 549 (1963) DOI
[5]
Vetchinkin, N. M. "Uniqueness of classes of positive quadratic forms, on which values of Hermite constants are reached for 6≤n≤8." Trudy Matematicheskogo Instituta imeni VA Steklova 152 (1980): 34-86.
[6]
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
[7]
L. Manivel, “Configurations of lines and models of Lie algebras”, (2005) arXiv:math/0507118
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Zoo Code ID: esix

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

Cite as:

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

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