{"paper":{"title":"On the List-Decodability of Random Linear Rank-Metric Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Nicolas Resch, Venkatesan Guruswami","submitted_at":"2017-10-31T14:42:39Z","abstract_excerpt":"The list-decodability of random linear rank-metric codes is shown to match that of random rank-metric codes. Specifically, an $\\mathbb{F}_q$-linear rank-metric code over $\\mathbb{F}_q^{m \\times n}$ of rate $R = (1-\\rho)(1-\\frac{n}{m}\\rho)-\\varepsilon$ is shown to be (with high probability) list-decodable up to fractional radius $\\rho \\in (0,1)$ with lists of size at most $\\frac{C_{\\rho,q}}{\\varepsilon}$, where $C_{\\rho,q}$ is a constant depending only on $\\rho$ and $q$. This matches the bound for random rank-metric codes (up to constant factors). The proof adapts the approach of Guruswami, H\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11516","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"}