{"author":[{"full_name":"Weiß, Charlene","id":"70420","first_name":"Charlene","last_name":"Weiß"}],"citation":{"ama":"Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. <i>Des Codes Cryptogr</i>. doi:<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>","ieee":"C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” <i>Des. Codes Cryptogr.</i>, doi: <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>.","mla":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>Des. Codes Cryptogr.</i>, doi:<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>.","short":"C. Weiß, Des. Codes Cryptogr. (n.d.).","bibtex":"@article{Weiß, title={Nontrivial $t$-designs in polar spaces exist for all $t$}, DOI={<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>}, journal={Des. Codes Cryptogr.}, author={Weiß, Charlene} }","apa":"Weiß, C. (n.d.). Nontrivial $t$-designs in polar spaces exist for all $t$. <i>Des. Codes Cryptogr.</i> <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">https://doi.org/10.1007/s10623-024-01471-1</a>","chicago":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>Des. Codes Cryptogr.</i>, n.d. <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">https://doi.org/10.1007/s10623-024-01471-1</a>."},"status":"public","date_created":"2024-01-08T14:39:54Z","publication_status":"submitted","department":[{"_id":"100"}],"abstract":[{"text":"A finite classical polar space of rank $n$ consists of the totally isotropic\r\nsubspaces of a finite vector space over $\\mathbb{F}_q$ equipped with a\r\nnondegenerate form such that $n$ is the maximal dimension of such a subspace. A\r\n$t$-$(n,k,\\lambda)$ design in a finite classical polar space of rank $n$ is a\r\ncollection $Y$ of totally isotropic $k$-spaces such that each totally isotropic\r\n$t$-space is contained in exactly $\\lambda$ members of $Y$. Nontrivial examples\r\nare currently only known for $t\\leq 2$. We show that $t$-$(n,k,\\lambda)$\r\ndesigns in polar spaces exist for all $t$ and $q$ provided that\r\n$k>\\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a\r\nprobabilistic method by Kuperberg, Lovett, and Peled, and it is thus\r\nnonconstructive.","lang":"eng"}],"language":[{"iso":"eng"}],"user_id":"70420","year":"2024","date_updated":"2024-08-28T14:06:47Z","doi":"10.1007/s10623-024-01471-1","_id":"50299","publication":"Des. Codes Cryptogr.","type":"journal_article","title":"Nontrivial $t$-designs in polar spaces exist for all $t$"}