{"paper":{"title":"Local decoding and testing of polynomials over grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Madhu Sudan, Mitali Bafna, Srikanth Srinivasan","submitted_at":"2017-09-18T16:40:54Z","abstract_excerpt":"The well-known DeMillo-Lipton-Schwartz-Zippel lemma says that $n$-variate polynomials of total degree at most $d$ over grids, i.e. sets of the form $A_1 \\times A_2 \\times \\cdots \\times A_n$, form error-correcting codes (of distance at least $2^{-d}$ provided $\\min_i\\{|A_i|\\}\\geq 2$). In this work we explore their local decodability and (tolerant) local testability. While these aspects have been studied extensively when $A_1 = \\cdots = A_n = \\mathbb{F}_q$ are the same finite field, the setting when $A_i$'s are not the full field does not seem to have been explored before.\n  In this work we focu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06036","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"}