{"paper":{"title":"An improved bound on the fraction of correctable deletions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Boris Bukh, Johan H{\\aa}stad, Venkatesan Guruswami","submitted_at":"2015-07-07T09:20:06Z","abstract_excerpt":"We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed $k \\ge 2$, we construct a family of codes over alphabet of size $k$ with positive rate, which allow efficient recovery from a worst-case deletion fraction approaching $1-\\frac{2}{k+\\sqrt k}$. In particular, for binary codes, we are able to recover a fraction of deletions approaching $1/(\\sqrt 2 +1)=\\sqrt 2-1 \\approx 0.414$. Previously, even non-constructively the largest deletion fraction known to be correctable with positive rate was $1-\\Theta(1/\\sqrt{k})$, and around $0.17$ for the binary case.\n  Our re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01719","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"}