On kissing numbers and spherical codes in high dimensions

被引：19

作者：

Jenssen, Matthew ^{[1
]}

Joos, Felix ^{[2
]}

Perkins, Will ^{[2
]}

机构：

[1] Univ Oxford, Oxford, England

[2] Univ Birmingham, Birmingham, W Midlands, England

来源：

ADVANCES IN MATHEMATICS | 2018年 / 335卷

基金：

英国工程与自然科学研究理事会;

关键词：

Kissing numbers; Spherical codes; High dimensional geometry; BOUNDS; ERROR;

D O I：

10.1016/j.aim.2018.07.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a lower bound of Omega(d(3/2) . (2/root 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 theta in high dimensions. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：307 / 321

页数：15

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