{"paper":{"title":"Explicit rank-metric codes list-decodable with optimal redundancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Carol Wang, Venkatesan Guruswami","submitted_at":"2013-11-27T19:35:46Z","abstract_excerpt":"We construct an explicit family of linear rank-metric codes over any field ${\\mathbb F}_h$ that enables efficient list decoding up to a fraction $\\rho$ of errors in the rank metric with a rate of $1-\\rho-\\epsilon$, for any desired $\\rho \\in (0,1)$ and $\\epsilon > 0$. Previously, a Monte Carlo construction of such codes was known, but this is in fact the first explicit construction of positive rate rank-metric codes for list decoding beyond the unique decoding radius.\n  Our codes are subcodes of the well-known Gabidulin codes, which encode linearized polynomials of low degree via their values a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7084","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"}