{"paper":{"title":"Stopping Sets of Algebraic Geometry Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Daqing Wan, Fang-Wei Fu, Jun Zhang","submitted_at":"2013-04-27T19:50:29Z","abstract_excerpt":"Stopping sets and stopping set distribution of a linear code play an important role in the performance analysis of iterative decoding for this linear code. Let $C$ be an $[n,k]$ linear code over $\\f$ with parity-check matrix $H$, where the rows of $H$ may be dependent. Let $[n]=\\{1,2,...,n\\}$ denote the set of column indices of $H$. A \\emph{stopping set} $S$ of $C$ with parity-check matrix $H$ is a subset of $[n]$ such that the restriction of $H$ to $S$ does not contain a row of weight 1. The \\emph{stopping set distribution} $\\{T_{i}(H)\\}_{i=0}^{n}$ enumerates the number of stopping sets with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7402","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"}