Bounds for the sum of distances of spherical sets of small size

被引：1

作者：

Barg, Alexander ^{[1
]}

Boyvalenkov, Peter ^{[2
]}

Stoyanova, Maya ^{[3
]}

机构：

[1] Univ Maryland, Dept ECE & ISR, College Pk, MD 20742 USA

[2] Bulgarian Acad Sci, Inst Math & Informat, 8 G Bonchev Str, Sofia 1113, Bulgaria

[3] Sofia Univ St Kliment Ohridski, Fac Math & Informat, 5 James Bourchier Blvd, Sofia 1164, Bulgaria

来源：

DISCRETE MATHEMATICS | 2023年 / 346卷 / 05期

关键词：

Spherical set; Linear programming bound; Universal energy bound; BINARY LINEAR CODES; EQUIANGULAR LINES; ENERGY; POINTS; DISTRIBUTIONS; ASYMPTOTICS;

D O I：

10.1016/j.disc.2023.113346

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive upper and lower bounds on the sum of distances of a spherical code of size N in n dimensions when N = O(n alpha), 0 < alpha 2. The bounds are derived by specializing recent general, universal bounds on energy of spherical sets. We discuss asymptotic behavior of our bounds along with several examples of codes whose sum of distances closely follows the upper bound.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：19

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