Bounds on sets with few distances

Authors:
Alexander Barg;Oleg R. Musin
Affiliations:
Dept. of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA and Institute for Problems of Information Transmission, Russian ...;Department of Mathematics, University of Texas at Brownsville, 80 Fort Brown, Brownsville, TX 78520, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

Citing 7
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Abstract

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.