{"paper":{"title":"On the List Decodability of Self-orthogonal Rank Metric Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shu Liu","submitted_at":"2018-01-22T10:41:16Z","abstract_excerpt":"V. Guruswami and N. Resch prove that the list decodability of $\\mathbb{F}_q$-linear rank metric codes is as good as that of random rank metric codes in~\\cite{venkat2017}. Due to the potential applications of self-orthogonal rank metric codes, we focus on list decoding of them. In this paper, we prove that with high probability, an $\\F_q$-linear self-orthogonal rank metric code over $\\mathbb{F}_q^{n\\times m}$ of rate $R=(1-\\tau)(1-\\frac{n}{m}\\tau)-\\epsilon$ is shown to be list decodable up to fractional radius $\\tau\\in(0,1)$ and small $\\epsilon\\in(0,1)$ with list size depending on $\\tau$ and $q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07033","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"}