{"paper":{"title":"The zero-rate threshold for adversarial bit-deletions is less than 1/2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ray Li, Venkatesan Guruswami, Xiaoyu He","submitted_at":"2021-06-09T17:45:34Z","abstract_excerpt":"We prove that there exists an absolute constant $\\delta>0$ such any binary code $C\\subset\\{0,1\\}^N$ tolerating $(1/2-\\delta)N$ adversarial deletions must satisfy $|C|\\le 2^{\\text{poly}\\log N}$ and thus have rate asymptotically approaching 0. This is the first constant fraction improvement over the trivial bound that codes tolerating $N/2$ adversarial deletions must have rate going to 0 asymptotically. Equivalently, we show that there exists absolute constants $A$ and $\\delta>0$ such that any set $C\\subset\\{0,1\\}^N$ of $2^{\\log^A N}$ binary strings must contain two strings $c$ and $c'$ whose lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05250","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.05250/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}