{"paper":{"title":"Combinatorial limitations of average-radius list-decoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Srivatsan Narayanan, Venkatesan Guruswami","submitted_at":"2012-02-27T22:28:23Z","abstract_excerpt":"We study certain combinatorial aspects of list-decoding, motivated by the exponential gap between the known upper bound (of $O(1/\\gamma)$) and lower bound (of $\\Omega_p(\\log (1/\\gamma))$) for the list-size needed to decode up to radius $p$ with rate $\\gamma$ away from capacity, i.e., $1-\\h(p)-\\gamma$ (here $p\\in (0,1/2)$ and $\\gamma > 0$). Our main result is the following:\n  We prove that in any binary code $C \\subseteq \\{0,1\\}^n$ of rate $1-\\h(p)-\\gamma$, there must exist a set $\\mathcal{L} \\subset C$ of $\\Omega_p(1/\\sqrt{\\gamma})$ codewords such that the average distance of the points in $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6086","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"}