{"paper":{"title":"Optimal cyclic $(r,\\delta)$ locally repairable codes with unbounded length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fang-Wei Fu, Weijun Fang","submitted_at":"2018-05-31T07:04:12Z","abstract_excerpt":"Locally repairable codes with locality $r$ ($r$-LRCs for short) were introduced by Gopalan et al. \\cite{1} to recover a failed node of the code from at most other $r$ available nodes. And then $(r,\\delta)$ locally repairable codes ($(r,\\delta)$-LRCs for short) were produced by Prakash et al. \\cite{2} for tolerating multiple failed nodes. An $r$-LRC can be viewed as an $(r,2)$-LRC. An $(r,\\delta)$-LRC is called optimal if it achieves the Singleton-type bound. It has been a great challenge to construct $q$-ary optimal $(r,\\delta)$-LRCs with length much larger than $q$. Surprisingly, Luo et al. \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12345","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"}