{"paper":{"title":"Bounds on sets with few distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MG"],"primary_cat":"math.CO","authors_text":"Alexander Barg, Oleg R. Musin","submitted_at":"2009-05-14T21:12:19Z","abstract_excerpt":"We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered:\n  (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of subsets;\n  (2) we refine the bound of Delsarte-Goethals-Seidel on the maximum size of spherical sets with few distances;\n  (3) we prove a new bound on codes with few distances in the Hamming space, improving an earlier result of Delsarte.\n  We also find the size of maximal binary codes and maximal constant-weight codes of small length with 2 and 3 distances."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2423","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}