Finding and Investigating Exact Spherical Codes

被引：1

作者：

Wang, Jeffrey

机构：

[1] Bellevue, WA, 98006

来源：

EXPERIMENTAL MATHEMATICS | 2009年 / 18卷 / 02期

关键词：

Spherical; code; energy; minimization; EQUAL CIRCLES; PACKING;

D O I：

10.1080/10586458.2009.10128893

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we present the results of computer searches using a variation of an energy-minimization algorithm used by Kottwitz for finding good spherical codes. We prove that exact codes exist by representing the inner products between the vectors as algebraic numbers. For selected interesting cases, we include detailed discussion of the configurations. Of particular interest are the 20-point code in R(6) and the 24-point code in R(7), each of which is the union of two cross-polytopes in parallel hyperplanes. Finally, we catalogue all of the codes we have found.

引用

页码：249 / 256

页数：8

共 10 条

[1] BACHOC C, 2007, ARXIV07083947
[2] BALLINGER B, 2007, ARXIVMATH0611451
[3] BUDDENHAGEN J, 1994, MULTIPLICITY SYMMETR
[4] THE CLOSEST PACKING OF EQUAL CIRCLES ON A SPHERE
CLARE, BW
KEPERT, DL
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1986, 405 (1829): : 329 - 344
[5] Ericson T., 2001, Codes on Euclidean spheres
[6] THE DENSEST PACKING OF EQUAL CIRCLES ON A SPHERE
KOTTWITZ, DA
[J]. ACTA CRYSTALLOGRAPHICA SECTION A, 1991, 47 : 158 - 165
[7] Leech J., 1957, Mathematical Gazette, V41, P81
[8] NURMELA KJ, 1995, RES REPORTS HELSIN A, V32
[9] Sloane N. J. A., 1994, TABLES SPHERICAL COD
[10] Tammes P. M. L., 1930, Recueil Des Travaux Botaniques Nerlandais, V27, P1

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