On kissing numbers and spherical codes in high dimensions

Matthew Jenssen; Felix Joos; Will Perkins

doi:10.1016/j.aim.2018.07.001

On kissing numbers and spherical codes in high dimensions

Matthew Jenssen, Felix Joos, Will Perkins

Mathematics

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Abstract

We prove a lower bound of Ω(d^3/2·(2/√3)^d) on the kissing number in dimension d. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor in the dimension. We obtain a similar linear factor improvement to the best known lower bound on the maximal size of a spherical code of acute angle θ in high dimensions.

Original language	English
Pages (from-to)	307-321
Number of pages	15
Journal	Advances in Mathematics
Volume	335
Early online date	17 Jul 2018
DOIs	https://doi.org/10.1016/j.aim.2018.07.001
Publication status	Published - 7 Sept 2018

Keywords

Kissing numbers
Spherical codes
High dimensional geometry

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AU - Perkins, Will

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AB - We prove a lower bound of Ω(d3/2·(2/√3)d) on the kissing number in dimension d. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor in the dimension. We obtain a similar linear factor improvement to the best known lower bound on the maximal size of a spherical code of acute angle θ in high dimensions.

KW - Kissing numbers

KW - Spherical codes

KW - High dimensional geometry

U2 - 10.1016/j.aim.2018.07.001

DO - 10.1016/j.aim.2018.07.001

M3 - Article

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JO - Advances in Mathematics

JF - Advances in Mathematics

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On kissing numbers and spherical codes in high dimensions

Abstract

Keywords

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