{"paper":{"title":"Computing coset leaders and leader codewords of binary codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"E. Mart\\'inez-Moro, I. M\\'arquez-Corbella, M. A. Borges-Trenard, M. Borges-Quintana","submitted_at":"2012-11-23T18:17:49Z","abstract_excerpt":"In this paper we use the Gr\\\"obner representation of a binary linear code $\\mathcal C$ to give efficient algorithms for computing the whole set of coset leaders, denoted by $\\mathrm{CL}(\\mathcal C)$ and the set of leader codewords, denoted by $\\mathrm L(\\mathcal C)$. The first algorithm could be adapted to provide not only the Newton and the covering radius of $\\mathcal C$ but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5568","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"}