Bounds on sets with few distances
Copyright policy )Bounds on sets with few distances
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
- Russian Academy of Science Russian Federation
- The University of Texas System United States
- University of Maryland United States
- University of Maryland, College Park United States
- Institute for Problems of Information Transmission Russian Federation
FOS: Computer and information sciences, Orthogonal polynomials, Computer Science - Information Theory, Information Theory (cs.IT), Extremal set theory, binary codes, spherical codes, Metric Geometry (math.MG), intersecting families, Intersecting families, distance transitive spaces, Theoretical Computer Science, Binary codes, Computational Theory and Mathematics, Mathematics - Metric Geometry, Spherical codes, FOS: Mathematics, Distance transitive spaces, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), orthogonal polynomials
FOS: Computer and information sciences, Orthogonal polynomials, Computer Science - Information Theory, Information Theory (cs.IT), Extremal set theory, binary codes, spherical codes, Metric Geometry (math.MG), intersecting families, Intersecting families, distance transitive spaces, Theoretical Computer Science, Binary codes, Computational Theory and Mathematics, Mathematics - Metric Geometry, Spherical codes, FOS: Mathematics, Distance transitive spaces, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), orthogonal polynomials
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