{"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/fooling-sets-and-rank-in-nonzero","title":"Fooling-sets and rank in nonzero characteristic (extended abstract)","arxiv_id":"1305.2468","date":"2013-05-02","proceeding":null,"authors":["Mirjam Friesen","Dirk Oliver Theis"],"abstract":"An n\\times n matrix M is called a fooling-set matrix of size n, if its diagonal entries are nonzero, whereas for every k\\ne \\ell we have M_{k,\\ell} M_{\\ell,k} = 0. Dietzfelbinger, Hromkovi\\v{c}, and Schnitger (1996) showed that n \\le (\\rk M)^2, regardless of over which field the rank is computed, and asked whether the exponent on \\rk M can be improved. We settle this question for nonzero characteristic by constructing a family of matrices for which the bound is asymptotically tight. The construction uses linear recurring sequences.","url_abs":"http://arxiv.org/abs/1305.2468v1","url_pdf":"http://arxiv.org/pdf/1305.2468v1.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":"fooling-sets-and-rank-in-nonzero","repo_url":"https://github.com/maehjam/maehjam.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}