{"paper":{"title":"Succinct Representation of Codes with Applications to Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Elena Grigorescu, Madhu Sudan, Tali Kaufman","submitted_at":"2009-05-18T15:55:38Z","abstract_excerpt":"Motivated by questions in property testing, we search for linear error-correcting codes that have the \"single local orbit\" property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every \"sparse\" binary code whose coordinates are indexed by elements of F_{2^n} for prime n, and whose symmetry group includes the group of non-singular affine transformations of F_{2^n} has the single local orbit property. (A code is said to be \"sparse\" if it contains polynomially many codewords in its block length.) In partic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2919","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":""},"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"}