{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bounds-and-constructions-for-linear-locally","title":"Bounds and Constructions for Linear Locally Repairable Codes over Binary Fields","arxiv_id":"1701.05989","date":"2017-01-21","proceeding":null,"authors":["Anyu Wang","Zhifang Zhang","Dongdai Lin"],"abstract":"For binary $[n,k,d]$ linear locally repairable codes (LRCs), two new upper bounds on $k$ are derived. The first one applies to LRCs with disjoint local repair groups, for general values of $n,d$ and locality $r$, containing some previously known bounds as special cases. The second one is based on solving an optimization problem and applies to LRCs with arbitrary structure of local repair groups. Particularly, an explicit bound is derived from the second bound when $d\\geq 5$. A specific comparison shows this explicit bound outperforms the Cadambe-Mazumdar bound for $5\\leq d\\leq 8$ and large values of $n$. Moreover, a construction of binary linear LRCs with $d\\geq6$ attaining our second bound is provided.","url_abs":"http://arxiv.org/abs/1701.05989v2","url_pdf":"http://arxiv.org/pdf/1701.05989v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"bounds-and-constructions-for-linear-locally","repo_url":"https://github.com/wangrabbit1987/Binary-LRC-Upper-Bound-Calculator","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}