Nonexistence of certain spherical designs of odd strengths and cardinalities

被引：11

作者：

Boyvalenkov, P

Danev, D

Nikova, S

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

[2] V Turnovo Univ, Dept Math & Informat, V Turnovo 5000, Bulgaria

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 1999年 / 21卷 / 01期

关键词：

Minimum Distance; Spherical Design; Nonexistence Argument;

D O I：

10.1007/PL00009406

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A spherical tau-design on Sn-1 is a finite set such that, for all polynomials f of degree at most tau, the average of f over the set is equal to the average of f over the sphere Sn-1. in this paper we obtain some necessary conditions for the existence of designs of odd strengths and cardinalities. This gives nonexistence results in many cases. Asymptotically, we derive a bound which is better than the corresponding estimation ensured by the Delsarte-Goethals-Seidel bound. We consider in detail the strengths tau = 3 and tau = 5 and obtain further nonexistence results in these cases. When the nonexistence argument does not work, we obtain bounds on the minimum distance of such designs.

引用

页码：143 / 156

页数：14