Bounds on sets with few distances

被引：13

作者：

Barg, Alexander ^{[1
,2
,3
]}

Musin, Oleg R. ^{[4
]}

机构：

[1] Univ Maryland, Dept Elect & Comp Engn, College Pk, MD 20742 USA

[2] Univ Maryland, Syst Res Inst, College Pk, MD 20742 USA

[3] Russian Acad Sci, Inst Problems Informat Transmiss, Moscow, Russia

[4] Univ Texas Brownsville, Dept Math, Brownsville, TX 78520 USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2011年 / 118卷 / 04期

基金：

美国国家科学基金会;

关键词：

Distance transitive spaces; Binary codes; Intersecting families; Orthogonal polynomials; Spherical codes; POLYNOMIALS; SYSTEMS;

D O I：

10.1016/j.jcta.2011.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: we improve the Ray-Chaudhuri-Wilson bound of the size of uniform intersecting families of subsets; we refine the bound of Delsarte-Goethals-Seidel on the maximum size of spherical sets with few distances; we prove a new bound on codes with few distances in the Hamming space, improving an earlier result of Delsarte. We also find the size of maximal binary codes and maximal constant-weight codes of small length with 2 and 3 distances. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1465 / 1474

页数：10

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