2009/05/31 by Alexander Barg, Oleg R. Musin · 1 citation
Computer Science · Mathematics · #Algorithm #Block code #Coding theory and cryptography #Combinatorics #Computer science #Discrete mathematics #Hamming bound #Hamming code #Hamming distance #Hamming space #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Mathematical analysis #Mathematics #Metric (unit) #Metric space #Space (punctuation) #Upper and lower bounds #cs.IT #math.CO #math.IT #math.MG
paper · pdf · doi:10.1016/j.jcta.2011.01.002
published as Journal of Combinatorial Theory Ser. A, 118 , no. 4, 2011, pp. 1465-1474, · 11 pages
arxiv created 2010/09/08 · openalex publication_date 2011/01/20 · arxiv updated 2011/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.