{"paper":{"title":"On List-decodability of Random Rank Metric Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Yang Ding","submitted_at":"2014-01-13T01:18:04Z","abstract_excerpt":"In the present paper, we consider list decoding for both random rank metric codes and random linear rank metric codes. Firstly, we show that, for arbitrary $0<R<1$ and $\\epsilon>0$ ($\\epsilon$ and $R$ are independent), if $0<\\frac{n}{m}\\leq \\epsilon$, then with high probability a random rank metric code in $F_{q}^{m\\times n}$ of rate $R$ can be list-decoded up to a fraction $(1-R-\\epsilon)$ of rank errors with constant list size $L$ satisfying $L\\leq O(1/\\epsilon)$. Moreover, if $\\frac{n}{m}\\geq\\Theta_R(\\epsilon)$, any rank metric code in $F_{q}^{m\\times n}$ with rate $R$ and decoding radius $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2693","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"}