{"paper":{"title":"Further results on multiple coverings of the farthest-off points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander A. Davydov, Daniele Bartoli, Fernanda Pambianco, Massimo Giulietti, Stefano Marcugini","submitted_at":"2015-06-01T08:44:54Z","abstract_excerpt":"Multiple coverings of the farthest-off points ($(R,\\mu)$-MCF codes) and the corresponding $(\\rho,\\mu)$-saturating sets in projective spaces $PG(N,q)$ are considered. We propose and develop some methods which allow us to obtain new small $(1,\\mu)$-saturating sets and short $(2,\\mu)$-MCF codes with $\\mu$-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly $1+1/cq$, $c\\ge1$). In particular, we provide new algebraic constructions and some bounds. Also, we classify minimal and optimal $(1,\\mu)$-saturating sets in $PG(2,q)$, $q$ small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00392","kind":"arxiv","version":1},"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"}