{"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/multilinear-algebra-for-distributed-storage","title":"Multilinear Algebra for Distributed Storage","arxiv_id":"2006.08911","date":"2020-06-16","proceeding":null,"authors":["Iwan Duursma","Xiao Li","Hsin-Po Wang"],"abstract":"An $(n, k, d, \\alpha, \\beta, M)$-ERRC (exact-repair regenerating code) is a collection of $n$ nodes used to store a file. For a file of total size $M$, each node stores $\\alpha$ symbols, any $k$ nodes recover the file, and any $d$ nodes repair any other node via sending out $\\beta$ symbols. We establish a multilinear algebra foundation to assemble $(n, k, d, \\alpha, \\beta, M)$-ERRCs for all meaningful $(n, k, d)$ tuples. Our ERRCs tie the $\\alpha/M$-versus-$\\beta/M$ trade-off with cascade codes, the best known construction for this trade-off. We give directions on how these ERRCs repair multiple failures.","url_abs":"http://arxiv.org/abs/2006.08911v1","url_pdf":"http://arxiv.org/pdf/2006.08911v1.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":"multilinear-algebra-for-distributed-storage","repo_url":"https://github.com/Symbol1/MoulinDistorage","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}