Bounds on sets with few distances

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Barg, Alexander^1,2,3  Musin, Oleg R.⁴ 

[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

关键词: Distance transitive spaces;    Binary codes;    Intersecting families;    Orthogonal polynomials;    Spherical codes;   

DOI  :  10.1016/j.jcta.2011.01.002

来源: Elsevier

【 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.

【 授权许可】

Free