Bounds on sets with few distances
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: (1) we improve the RayChaudhuriWilson bound of the size of uniform intersecting families of subsets; (2) we refine the bound of DelsarteGoethalsSeidel on the maximum size of spherical sets with few distances; (3) 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 constantweight codes of small length with 2 and 3 distances.
 Publication:

arXiv eprints
 Pub Date:
 May 2009
 arXiv:
 arXiv:0905.2423
 Bibcode:
 2009arXiv0905.2423B
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Information Theory;
 Mathematics  Metric Geometry
 EPrint:
 11 pages