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 Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of subsets; (2) we refine the bound of Delsarte-Goethals-Seidel 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 constant-weight codes of small length with 2 and 3 distances.

11 pages

References in corpus (2)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• New upper bound for the cardinalities of $s$-distance sets on the unit sphere

Cited by in corpus (6)

• Upper bounds for $s$-distance sets and equiangular lines
• Constructions of biangular tight frames and their relationships with equiangular tight frames
• Semidefinite programming bounds for binary codes from a split Terwilliger algebra
• On the size of maximal binary codes with 2, 3, and 4 distances
• Maximal $2$-distance sets containing the regular simplex
• Bounds on three- and higher-distance sets