[{"publication_status":"published","year":"2025","page":"971 - 981","intvolume":"        93","citation":{"ieee":"C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” <i>Des. Codes Cryptogr.</i>, vol. 93, pp. 971–981, 2025, doi: <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">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> 93 (2025): 971–81. <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">https://doi.org/10.1007/s10623-024-01471-1</a>.","ama":"Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. <i>Des Codes Cryptogr</i>. 2025;93:971-981. 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. 93 (2025) 971–981.","bibtex":"@article{Weiß_2025, title={Nontrivial $t$-designs in polar spaces exist for all $t$}, volume={93}, 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}, year={2025}, pages={971–981} }","mla":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>Des. Codes Cryptogr.</i>, vol. 93, 2025, pp. 971–81, doi:<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>.","apa":"Weiß, C. (2025). Nontrivial $t$-designs in polar spaces exist for all $t$. <i>Des. Codes Cryptogr.</i>, <i>93</i>, 971–981. <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">https://doi.org/10.1007/s10623-024-01471-1</a>"},"date_updated":"2026-02-25T13:51:50Z","volume":93,"author":[{"full_name":"Weiß, Charlene","id":"70420","last_name":"Weiß","first_name":"Charlene"}],"date_created":"2024-01-08T14:39:54Z","title":"Nontrivial $t$-designs in polar spaces exist for all $t$","doi":"10.1007/s10623-024-01471-1","publication":"Des. Codes Cryptogr.","type":"journal_article","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"}],"status":"public","_id":"50299","department":[{"_id":"100"}],"user_id":"70420","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"user_id":"91965","department":[{"_id":"100"}],"external_id":{"arxiv":["2507.00813"]},"_id":"60491","status":"public","abstract":[{"text":"We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph $K_{2n}$. We show that they are special subsets of the association scheme obtained from the Gelfand pair $(S_{2n},S_2 \\wr S_n)$. This unifies and extends results by Cameron (1976) and gives rise to new existence and non-existence results. Our methods involve working in the group algebra $\\mathbb{C}[S_{2n}]$ and using the representation theory of $S_{2n}$.","lang":"eng"}],"type":"preprint","title":"On the association scheme of perfect matchings and their designs","date_created":"2025-07-02T07:37:23Z","author":[{"last_name":"Klawuhn","orcid":"0009-0009-7736-4885","full_name":"Klawuhn, Lukas-André Dominik","id":"91965","first_name":"Lukas-André Dominik"},{"last_name":"Bamberg","full_name":"Bamberg, John","first_name":"John"}],"date_updated":"2025-07-02T07:47:09Z","citation":{"chicago":"Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs,” 2025.","ieee":"L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings and their designs.” 2025.","ama":"Klawuhn L-AD, Bamberg J. On the association scheme of perfect matchings and their designs. Published online 2025.","short":"L.-A.D. Klawuhn, J. Bamberg, (2025).","bibtex":"@article{Klawuhn_Bamberg_2025, title={On the association scheme of perfect matchings and their designs}, author={Klawuhn, Lukas-André Dominik and Bamberg, John}, year={2025} }","mla":"Klawuhn, Lukas-André Dominik, and John Bamberg. <i>On the Association Scheme of Perfect Matchings and Their Designs</i>. 2025.","apa":"Klawuhn, L.-A. D., &#38; Bamberg, J. (2025). <i>On the association scheme of perfect matchings and their designs</i>."},"year":"2025"},{"page":"36","citation":{"apa":"Klawuhn, L.-A. D., Huczynska, S., &#38; Paterson, M. (2025). <i>The Intersection Distribution: New Results and Perspectives</i>.","bibtex":"@article{Klawuhn_Huczynska_Paterson_2025, title={The Intersection Distribution: New Results and Perspectives}, author={Klawuhn, Lukas-André Dominik and Huczynska, Sophie and Paterson, Maura}, year={2025} }","mla":"Klawuhn, Lukas-André Dominik, et al. <i>The Intersection Distribution: New Results and Perspectives</i>. 2025.","short":"L.-A.D. Klawuhn, S. Huczynska, M. Paterson, (2025).","ama":"Klawuhn L-AD, Huczynska S, Paterson M. The Intersection Distribution: New Results and Perspectives. Published online 2025.","chicago":"Klawuhn, Lukas-André Dominik, Sophie Huczynska, and Maura Paterson. “The Intersection Distribution: New Results and Perspectives,” 2025.","ieee":"L.-A. D. Klawuhn, S. Huczynska, and M. Paterson, “The Intersection Distribution: New Results and Perspectives.” 2025."},"year":"2025","title":"The Intersection Distribution: New Results and Perspectives","author":[{"first_name":"Lukas-André Dominik","id":"91965","full_name":"Klawuhn, Lukas-André Dominik","orcid":"0009-0009-7736-4885","last_name":"Klawuhn"},{"last_name":"Huczynska","full_name":"Huczynska, Sophie","first_name":"Sophie"},{"first_name":"Maura","last_name":"Paterson","full_name":"Paterson, Maura"}],"date_created":"2025-10-08T14:52:20Z","date_updated":"2025-12-19T11:23:10Z","status":"public","abstract":[{"lang":"eng","text":"Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a polynomial with a set of lines, and a geometric interpretation via a (q+1)-set possessing an internal nucleus, the concepts have proved their usefulness as a new way to view various long-standing problems, and have applications in areas such as Kakeya sets. In this paper, by exploiting connections with diverse areas including the theory of algebraic curves, cyclotomy and the enumeration of irreducible polynomials, we establish new results and resolve various Open Problems of Li and Pott. We prove geometric results which shed new light on the relationship between intersection distribution and projective equivalence of polynomials, and algebraic results which describe and characterise the degree of Sf - the index of the largest non-zero entry in the intersection distribution of f. We provide new insights into the non-hitting spectrum, and show the limitations of the non-hitting index as a tool for characterisation. Finally, the benefits provided by the connections to other areas are evidenced in two short new proofs of the cubic case. "}],"type":"preprint","language":[{"iso":"eng"}],"department":[{"_id":"100"}],"user_id":"91965","external_id":{"arxiv":["2510.04675"]},"_id":"61759"},{"year":"2025","citation":{"ama":"Devillers A, Giudici M, Hawtin DR, Klawuhn L-AD, Morgan L. Linear dimension of group actions. Published online 2025.","chicago":"Devillers, Alice, Michael Giudici, Daniel R. Hawtin, Lukas-André Dominik Klawuhn, and Luke Morgan. “Linear Dimension of Group Actions,” 2025.","ieee":"A. Devillers, M. Giudici, D. R. Hawtin, L.-A. D. Klawuhn, and L. Morgan, “Linear dimension of group actions.” 2025.","mla":"Devillers, Alice, et al. <i>Linear Dimension of Group Actions</i>. 2025.","short":"A. Devillers, M. Giudici, D.R. Hawtin, L.-A.D. Klawuhn, L. Morgan, (2025).","bibtex":"@article{Devillers_Giudici_Hawtin_Klawuhn_Morgan_2025, title={Linear dimension of group actions}, author={Devillers, Alice and Giudici, Michael and Hawtin, Daniel R. and Klawuhn, Lukas-André Dominik and Morgan, Luke}, year={2025} }","apa":"Devillers, A., Giudici, M., Hawtin, D. R., Klawuhn, L.-A. D., &#38; Morgan, L. (2025). <i>Linear dimension of group actions</i>."},"date_updated":"2025-12-19T11:23:41Z","author":[{"first_name":"Alice","last_name":"Devillers","full_name":"Devillers, Alice"},{"last_name":"Giudici","full_name":"Giudici, Michael","first_name":"Michael"},{"first_name":"Daniel R.","last_name":"Hawtin","full_name":"Hawtin, Daniel R."},{"id":"91965","full_name":"Klawuhn, Lukas-André Dominik","orcid":"0009-0009-7736-4885","last_name":"Klawuhn","first_name":"Lukas-André Dominik"},{"first_name":"Luke","full_name":"Morgan, Luke","last_name":"Morgan"}],"date_created":"2025-12-19T11:20:46Z","title":"Linear dimension of group actions","type":"preprint","abstract":[{"text":"Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how small the matrices in such a linear representation can be. The minimal dimension of such a representation is the \\emph{linear dimension of the group action} and this has applications in cryptography and cryptosystems.\r\n\r\nWe develop the idea of linear dimension from an algebraic point of view by using the theory of permutation modules. We give structural results about representations of minimal dimension and investigate the implications of faithfulness, transitivity and primitivity on the linear dimension. Furthermore, we compute the linear dimension of several classes of finite primitive permutation groups. We also study wreath products, allowing us to determine the linear dimension of imprimitive group actions. Finally, we give the linear dimension of almost simple finite $2$-transitive groups, some of which may be used for further applications in cryptography. Our results also open up many new questions about linear representations of group actions.","lang":"eng"}],"status":"public","_id":"63384","external_id":{"arxiv":["2512.16079"]},"user_id":"91965","department":[{"_id":"100"}],"language":[{"iso":"eng"}]},{"volume":307,"author":[{"first_name":"Alena","last_name":"Ernst","id":"46953","full_name":"Ernst, Alena"},{"full_name":"Schmidt, Kai-Uwe","last_name":"Schmidt","first_name":"Kai-Uwe"}],"date_created":"2024-04-17T12:26:51Z","date_updated":"2024-06-17T10:04:29Z","doi":"10.1007/s00209-024-03511-x","title":"Transitivity in finite general linear groups","issue":"45","intvolume":"       307","citation":{"ama":"Ernst A, Schmidt K-U. Transitivity in finite general linear groups. <i>Mathematische Zeitschrift</i>. 2024;307(45). doi:<a href=\"https://doi.org/10.1007/s00209-024-03511-x\">10.1007/s00209-024-03511-x</a>","chicago":"Ernst, Alena, and Kai-Uwe Schmidt. “Transitivity in Finite General Linear Groups.” <i>Mathematische Zeitschrift</i> 307, no. 45 (2024). <a href=\"https://doi.org/10.1007/s00209-024-03511-x\">https://doi.org/10.1007/s00209-024-03511-x</a>.","ieee":"A. Ernst and K.-U. Schmidt, “Transitivity in finite general linear groups,” <i>Mathematische Zeitschrift</i>, vol. 307, no. 45, 2024, doi: <a href=\"https://doi.org/10.1007/s00209-024-03511-x\">10.1007/s00209-024-03511-x</a>.","apa":"Ernst, A., &#38; Schmidt, K.-U. (2024). Transitivity in finite general linear groups. <i>Mathematische Zeitschrift</i>, <i>307</i>(45). <a href=\"https://doi.org/10.1007/s00209-024-03511-x\">https://doi.org/10.1007/s00209-024-03511-x</a>","short":"A. Ernst, K.-U. Schmidt, Mathematische Zeitschrift 307 (2024).","mla":"Ernst, Alena, and Kai-Uwe Schmidt. “Transitivity in Finite General Linear Groups.” <i>Mathematische Zeitschrift</i>, vol. 307, no. 45, 2024, doi:<a href=\"https://doi.org/10.1007/s00209-024-03511-x\">10.1007/s00209-024-03511-x</a>.","bibtex":"@article{Ernst_Schmidt_2024, title={Transitivity in finite general linear groups}, volume={307}, DOI={<a href=\"https://doi.org/10.1007/s00209-024-03511-x\">10.1007/s00209-024-03511-x</a>}, number={45}, journal={Mathematische Zeitschrift}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2024} }"},"year":"2024","department":[{"_id":"100"}],"user_id":"46953","_id":"53534","language":[{"iso":"eng"}],"publication":"Mathematische Zeitschrift","type":"journal_article","status":"public","abstract":[{"text":"It is known that the notion of a transitive subgroup of a permutation group\r\n$G$ extends naturally to subsets of $G$. We consider subsets of the general\r\nlinear group $\\operatorname{GL}(n,q)$ acting transitively on flag-like\r\nstructures, which are common generalisations of $t$-dimensional subspaces of\r\n$\\mathbb{F}_q^n$ and bases of $t$-dimensional subspaces of $\\mathbb{F}_q^n$. We\r\ngive structural characterisations of transitive subsets of\r\n$\\operatorname{GL}(n,q)$ using the character theory of $\\operatorname{GL}(n,q)$\r\nand interpret such subsets as designs in the conjugacy class association\r\nscheme of $\\operatorname{GL}(n,q)$. In particular we generalise a theorem of\r\nPerin on subgroups of $\\operatorname{GL}(n,q)$ acting transitively on\r\n$t$-dimensional subspaces. We survey transitive subgroups of\r\n$\\operatorname{GL}(n,q)$, showing that there is no subgroup of\r\n$\\operatorname{GL}(n,q)$ with $1<t<n$ acting transitively on $t$-dimensional\r\nsubspaces unless it contains $\\operatorname{SL}(n,q)$ or is one of two\r\nexceptional groups. On the other hand, for all fixed $t$, we show that there\r\nexist nontrivial subsets of $\\operatorname{GL}(n,q)$ that are transitive on\r\nlinearly independent $t$-tuples of $\\mathbb{F}_q^n$, which also shows the\r\nexistence of nontrivial subsets of $\\operatorname{GL}(n,q)$ that are transitive\r\non more general flag-like structures. We establish connections with orthogonal\r\npolynomials, namely the Al-Salam-Carlitz polynomials, and generalise a result\r\nby Rudvalis and Shinoda on the distribution of the number of fixed points of\r\nthe elements in $\\operatorname{GL}(n,q)$. Many of our results can be\r\ninterpreted as $q$-analogs of corresponding results for the symmetric group.","lang":"eng"}]},{"author":[{"last_name":"Klawuhn","orcid":"0009-0009-7736-4885","id":"91965","full_name":"Klawuhn, Lukas-André Dominik","first_name":"Lukas-André Dominik"},{"first_name":"Kai-Uwe","last_name":"Schmidt","full_name":"Schmidt, Kai-Uwe"}],"date_created":"2024-10-08T13:14:45Z","date_updated":"2024-11-15T12:34:03Z","title":"Transitivity in wreath products with symmetric groups","citation":{"ama":"Klawuhn L-AD, Schmidt K-U. Transitivity in wreath products with symmetric groups. <i>arXiv:240920495</i>. Published online 2024.","chicago":"Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath Products with Symmetric Groups.” <i>ArXiv:2409.20495</i>, 2024.","ieee":"L.-A. D. Klawuhn and K.-U. Schmidt, “Transitivity in wreath products with symmetric groups,” <i>arXiv:2409.20495</i>. 2024.","mla":"Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath Products with Symmetric Groups.” <i>ArXiv:2409.20495</i>, 2024.","short":"L.-A.D. Klawuhn, K.-U. Schmidt, ArXiv:2409.20495 (2024).","bibtex":"@article{Klawuhn_Schmidt_2024, title={Transitivity in wreath products with symmetric groups}, journal={arXiv:2409.20495}, author={Klawuhn, Lukas-André Dominik and Schmidt, Kai-Uwe}, year={2024} }","apa":"Klawuhn, L.-A. D., &#38; Schmidt, K.-U. (2024). Transitivity in wreath products with symmetric groups. In <i>arXiv:2409.20495</i>."},"page":"38","year":"2024","user_id":"91965","department":[{"_id":"100"}],"_id":"56429","external_id":{"arxiv":["2409.20495"]},"language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:2409.20495","status":"public","abstract":[{"text":"It is known that the notion of a transitive subgroup of a permutation group\r\n$P$ extends naturally to the subsets of $P$. We study transitive subsets of the\r\nwreath product $G \\wr S_n$, where $G$ is a finite abelian group. This includes\r\nthe hyperoctahedral group for $G=C_2$. We give structural characterisations of\r\ntransitive subsets using the character theory of $G \\wr S_n$ and interpret such\r\nsubsets as designs in the conjugacy class association scheme of $G \\wr S_n$. In\r\nparticular, we prove a generalisation of the Livingstone-Wagner theorem and\r\ngive explicit constructions of transitive sets. Moreover, we establish\r\nconnections to orthogonal polynomials, namely the Charlier polynomials, and use\r\nthem to study codes and designs in $C_r \\wr S_n$. Many of our results extend\r\nresults about the symmetric group $S_n$.","lang":"eng"}]},{"doi":"10.5070/c63160424","title":"Packings and Steiner systems in polar spaces","author":[{"last_name":"Schmidt","full_name":"Schmidt, Kai-Uwe","first_name":"Kai-Uwe"},{"first_name":"Charlene","last_name":"Weiß","full_name":"Weiß, Charlene","id":"70420"}],"date_created":"2024-01-08T14:33:54Z","volume":3,"date_updated":"2024-01-08T14:39:20Z","citation":{"ama":"Schmidt K-U, Weiß C. Packings and Steiner systems in polar spaces. <i>Combinatorial Theory</i>. 2023;3(1). doi:<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>","ieee":"K.-U. Schmidt and C. Weiß, “Packings and Steiner systems in polar spaces,” <i>Combinatorial Theory</i>, vol. 3, no. 1, 2023, doi: <a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>.","chicago":"Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar Spaces.” <i>Combinatorial Theory</i> 3, no. 1 (2023). <a href=\"https://doi.org/10.5070/c63160424\">https://doi.org/10.5070/c63160424</a>.","apa":"Schmidt, K.-U., &#38; Weiß, C. (2023). Packings and Steiner systems in polar spaces. <i>Combinatorial Theory</i>, <i>3</i>(1). <a href=\"https://doi.org/10.5070/c63160424\">https://doi.org/10.5070/c63160424</a>","bibtex":"@article{Schmidt_Weiß_2023, title={Packings and Steiner systems in polar spaces}, volume={3}, DOI={<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>}, number={1}, journal={Combinatorial Theory}, author={Schmidt, Kai-Uwe and Weiß, Charlene}, year={2023} }","mla":"Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar Spaces.” <i>Combinatorial Theory</i>, vol. 3, no. 1, 2023, doi:<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>.","short":"K.-U. Schmidt, C. Weiß, Combinatorial Theory 3 (2023)."},"intvolume":"         3","year":"2023","issue":"1","publication_status":"published","language":[{"iso":"eng"}],"user_id":"70420","department":[{"_id":"100"}],"_id":"50298","status":"public","abstract":[{"lang":"eng","text":"A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces such that each totally isotropic $t$-space is contained in exactly one member of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost complete classification of such $t$-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces."}],"type":"journal_article","publication":"Combinatorial Theory"},{"doi":"10.1002/jcd.21903","title":"Existence of small ordered orthogonal arrays","author":[{"first_name":"Kai‐Uwe","full_name":"Schmidt, Kai‐Uwe","last_name":"Schmidt"},{"first_name":"Charlene","id":"70420","full_name":"Weiß, Charlene","last_name":"Weiß"}],"date_created":"2024-01-08T14:25:28Z","volume":31,"publisher":"Wiley","date_updated":"2024-01-08T14:38:53Z","citation":{"ama":"Schmidt K, Weiß C. Existence of small ordered orthogonal arrays. <i>Journal of Combinatorial Designs</i>. 2023;31(9):422-431. doi:<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>","chicago":"Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal Arrays.” <i>Journal of Combinatorial Designs</i> 31, no. 9 (2023): 422–31. <a href=\"https://doi.org/10.1002/jcd.21903\">https://doi.org/10.1002/jcd.21903</a>.","ieee":"K. Schmidt and C. Weiß, “Existence of small ordered orthogonal arrays,” <i>Journal of Combinatorial Designs</i>, vol. 31, no. 9, pp. 422–431, 2023, doi: <a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>.","short":"K. Schmidt, C. Weiß, Journal of Combinatorial Designs 31 (2023) 422–431.","bibtex":"@article{Schmidt_Weiß_2023, title={Existence of small ordered orthogonal arrays}, volume={31}, DOI={<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>}, number={9}, journal={Journal of Combinatorial Designs}, publisher={Wiley}, author={Schmidt, Kai‐Uwe and Weiß, Charlene}, year={2023}, pages={422–431} }","mla":"Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal Arrays.” <i>Journal of Combinatorial Designs</i>, vol. 31, no. 9, Wiley, 2023, pp. 422–31, doi:<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>.","apa":"Schmidt, K., &#38; Weiß, C. (2023). Existence of small ordered orthogonal arrays. <i>Journal of Combinatorial Designs</i>, <i>31</i>(9), 422–431. <a href=\"https://doi.org/10.1002/jcd.21903\">https://doi.org/10.1002/jcd.21903</a>"},"page":"422-431","intvolume":"        31","year":"2023","issue":"9","publication_status":"published","language":[{"iso":"eng"}],"user_id":"70420","department":[{"_id":"100"}],"_id":"50297","status":"public","abstract":[{"text":"We show that there exist ordered orthogonal arrays, whose sizes deviate from the Rao bound by a factor that is polynomial in the parameters of the ordered orthogonal array. The proof is nonconstructive and based on a probabilistic method due to Kuperberg, Lovett and Peled.","lang":"eng"}],"type":"journal_article","publication":"Journal of Combinatorial Designs"},{"date_updated":"2024-01-08T14:46:14Z","author":[{"first_name":"Charlene","full_name":"Weiß, Charlene","id":"70420","last_name":"Weiß"}],"date_created":"2024-01-08T14:42:12Z","title":"Linear programming bounds in classical association schemes","doi":"10.17619/UNIPB/1-1672","year":"2023","citation":{"apa":"Weiß, C. (2023). <i>Linear programming bounds in classical association schemes</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1672\">https://doi.org/10.17619/UNIPB/1-1672</a>","short":"C. Weiß, Linear Programming Bounds in Classical Association Schemes, 2023.","mla":"Weiß, Charlene. <i>Linear Programming Bounds in Classical Association Schemes</i>. 2023, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>.","bibtex":"@book{Weiß_2023, title={Linear programming bounds in classical association schemes}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>}, author={Weiß, Charlene}, year={2023} }","ama":"Weiß C. <i>Linear Programming Bounds in Classical Association Schemes</i>.; 2023. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>","ieee":"C. Weiß, <i>Linear programming bounds in classical association schemes</i>. 2023.","chicago":"Weiß, Charlene. <i>Linear Programming Bounds in Classical Association Schemes</i>, 2023. <a href=\"https://doi.org/10.17619/UNIPB/1-1672\">https://doi.org/10.17619/UNIPB/1-1672</a>."},"_id":"50300","department":[{"_id":"100"}],"user_id":"70420","language":[{"iso":"eng"}],"type":"dissertation","abstract":[{"lang":"eng","text":"Digital communications relies heavily on the usage of different types of codes. Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs of binary codes and binary codes with constant weight. All these codes can be viewed as subsets of classical association schemes. A central coding-theoretic problem is to derive upper bounds for the size of codes. This thesis investigates Delsartes powerful linear program whose optimum is precisely such a bound for codes in association schemes. The linear programs for binary codes and binary constant-weight codes have been extensively studied since the 1970s, but their optimum is still unknown. We determine in a unified way the optimum of the linear program in several ordinary q-analogs as well as in their affine counterparts. In particular, bounds and constructions for codes in polar spaces are established, where the bounds are sharp up to a constant factor in many cases. Moreover, based on these results, an almost complete classification of Steiner systems in polar spaces is provided by showing that they could only exist in some corner cases."}],"status":"public"},{"date_updated":"2024-05-07T08:29:59Z","publisher":"Cambridge University Press (CUP)","date_created":"2024-04-17T12:23:18Z","author":[{"first_name":"Alena","last_name":"Ernst","full_name":"Ernst, Alena","id":"46953"},{"full_name":"Schmidt, Kai-Uwe","last_name":"Schmidt","first_name":"Kai-Uwe"}],"volume":175,"title":"Intersection theorems for finite general linear groups","doi":"10.1017/s0305004123000075","publication_status":"published","publication_identifier":{"issn":["0305-0041","1469-8064"]},"issue":"1","year":"2023","citation":{"short":"A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 129–160.","mla":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, Cambridge University Press (CUP), 2023, pp. 129–60, doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","bibtex":"@article{Ernst_Schmidt_2023, title={Intersection theorems for finite general linear groups}, volume={175}, DOI={<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2023}, pages={129–160} }","apa":"Ernst, A., &#38; Schmidt, K.-U. (2023). Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, <i>175</i>(1), 129–160. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>","ama":"Ernst A, Schmidt K-U. Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2023;175(1):129-160. doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>","ieee":"A. Ernst and K.-U. Schmidt, “Intersection theorems for finite general linear groups,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, pp. 129–160, 2023, doi: <a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","chicago":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i> 175, no. 1 (2023): 129–60. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>."},"intvolume":"       175","page":"129-160","_id":"53533","user_id":"46953","department":[{"_id":"100"}],"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","status":"public"}]