{"paper":{"title":"On the List-Decodability of Random Self-Orthogonal Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Lingfei Jin, Xiande Zhang","submitted_at":"2016-11-21T07:46:00Z","abstract_excerpt":"In 2011, Guruswami-H{\\aa}stad-Kopparty \\cite{Gru} showed that the list-decodability of random linear codes is as good as that of general random codes. In the present paper, we further strengthen the result by showing that the list-decodability of random {\\it Euclidean self-orthogonal} codes is as good as that of general random codes as well, i.e., achieves the classical Gilbert-Varshamov bound. Specifically, we show that, for any fixed finite field $\\F_q$, error fraction $\\delta\\in (0,1-1/q)$ satisfying $1-H_q(\\delta)\\le \\frac12$ and small $\\epsilon>0$, with high probability a random Euclidean"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06673","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"}