{"paper":{"title":"An Exponential Lower Bound for Linear 3-Query Locally Correctable Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Peter Manohar, Pravesh K. Kothari","submitted_at":"2023-11-01T14:55:04Z","abstract_excerpt":"We prove that the blocklength $n$ of a linear $3$-query locally correctable code (LCC) $\\mathcal{L} \\colon {\\mathbb F}^k \\to {\\mathbb F}^n$ with distance $\\delta$ must be at least $n \\geq 2^{\\Omega\\left(\\left(\\frac{\\delta^2 k}{(|{\\mathbb F}|-1)^2}\\right)^{1/8}\\right)}$. In particular, the blocklength of a linear $3$-query LCC with constant distance over any small field grows exponentially with $k$. This improves on the best prior lower bound of $n \\geq \\tilde{\\Omega}(k^3)$ [AGKM23], which holds even for the weaker setting of $3$-query locally decodable codes (LDCs), and comes close to matching"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00558","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.00558/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"}