{"paper":{"title":"New Constructions for Query-Efficient Locally Decodable Codes of Subexponential Length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"cs.CC","authors_text":"Toshiya Itoh, Yasuhiro Suzuki","submitted_at":"2008-10-25T04:53:23Z","abstract_excerpt":"A $(k,\\delta,\\epsilon)$-locally decodable code $C: F_{q}^{n} \\to F_{q}^{N}$ is an error-correcting code that encodes each message $\\vec{x}=(x_{1},x_{2},...,x_{n}) \\in F_{q}^{n}$ to $C(\\vec{x}) \\in F_{q}^{N}$ and has the following property: For any $\\vec{y} \\in {\\bf F}_{q}^{N}$ such that $d(\\vec{y},C(\\vec{x})) \\leq \\delta N$ and each $1 \\leq i \\leq n$, the symbol $x_{i}$ of $\\vec{x}$ can be recovered with probability at least $1-\\epsilon$ by a randomized decoding algorithm looking only at $k$ coordinates of $\\vec{y}$. The efficiency of a $(k,\\delta,\\epsilon)$-locally decodable code $C: F_{q}^{n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4576","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"}