Spherical sharp configuration[14] 

Description

A spherical code that is a spherical design of strength \(2m-1\) for some \(m\) and that has \(m\) distances between distinct points. All known spherical sharp configrations are either obtained from the Leech or \(E_8\) lattice, certain regular polytopes, or are CGS isotropic subspace spherical codes.

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References

[1]
V. I. Levenshtein, "On choosing polynomials to obtain bounds in packing problems." Proc. Seventh All-Union Conf. on Coding Theory and Information Transmission, Part II, Moscow, Vilnius. 1978.
[2]
V. I. Levenshtein, “On bounds for packings in n-dimensional Euclidean space”, Dokl. Akad. Nauk SSSR, 245:6 (1979), 1299–1303
[3]
V. I. Levenshtein, “Designs as maximum codes in polynomial metric spaces”, Acta Applicandae Mathematicae 29, 1 (1992) DOI
[4]
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
[5]
Andreev, Nikolay N. "An extremal property of the icosahedron." East J. Approx 2.4 (1996): 459-462.
[6]
A. V. KOLUSHOV and V. A. YUDIN, “On Korkin-Zolotarev’s construction”, Discrete Mathematics and Applications 4, (1994) DOI
[7]
Andreev, N. N. Location of points on a sphere with minimal energy. (Russian) Tr. Mat. Inst. Steklova 219 (1997), Teor. Priblizh. Garmon. Anal., 27–31; translation in Proc. Steklov Inst. Math. 1997, no. 4(219), 20–24
[8]
B. Ballinger et al., “Experimental Study of Energy-Minimizing Point Configurations on Spheres”, Experimental Mathematics 18, 257 (2009) arXiv:math/0611451 DOI
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Zoo Code ID: sharp_config

Cite as:
“Spherical sharp configuration”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/sharp_config
BibTeX:
@incollection{eczoo_sharp_config, title={Spherical sharp configuration}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/sharp_config} }
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“Spherical sharp configuration”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/sharp_config

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