{"paper":{"title":"Optimal locally repairable codes of distance $3$ and $4$ via cyclic codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Chen Yuan, Yuan Luo","submitted_at":"2018-01-11T03:26:40Z","abstract_excerpt":"Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code {\\it optimal} if it achieves the Singleton-type bound). In the breakthrough work of \\cite{TB14}, several classes of optimal locally repairable codes were constructed via subcodes of Reed-Solomon codes. Thus, the lengths of the codes given in \\cite{TB14} are upper bounded by the code alphabet size $q$. Recently, it was proved through extension of construction in \\cite{TB14} that length of $q$-ary optimal locally repairable codes can be $q+1$ in \\cite{JMX17}. Surprisingly,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03623","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"}