[{"user_id":"91965","volume":114,"_id":"61759","publisher":"Elsevier","status":"public","oa":"1","citation":{"chicago":"Klawuhn, Lukas-André Dominik, Sophie Huczynska, and Maura Paterson. “The Intersection Distribution: New Results and Perspectives.” <i>Finite Fields and Their Applications</i> 114 (2026). <a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">https://doi.org/10.1016/j.ffa.2026.102828</a>.","short":"L.-A.D. Klawuhn, S. Huczynska, M. Paterson, Finite Fields and Their Applications 114 (2026).","ieee":"L.-A. D. Klawuhn, S. Huczynska, and M. Paterson, “The Intersection Distribution: New Results and Perspectives,” <i>Finite Fields and Their Applications</i>, vol. 114, Art. no. 102828, 2026, doi: <a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">10.1016/j.ffa.2026.102828</a>.","apa":"Klawuhn, L.-A. D., Huczynska, S., &#38; Paterson, M. (2026). The Intersection Distribution: New Results and Perspectives. <i>Finite Fields and Their Applications</i>, <i>114</i>, Article 102828. <a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">https://doi.org/10.1016/j.ffa.2026.102828</a>","bibtex":"@article{Klawuhn_Huczynska_Paterson_2026, title={The Intersection Distribution: New Results and Perspectives}, volume={114}, DOI={<a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">10.1016/j.ffa.2026.102828</a>}, number={102828}, journal={Finite Fields and Their Applications}, publisher={Elsevier}, author={Klawuhn, Lukas-André Dominik and Huczynska, Sophie and Paterson, Maura}, year={2026} }","ama":"Klawuhn L-AD, Huczynska S, Paterson M. The Intersection Distribution: New Results and Perspectives. <i>Finite Fields and Their Applications</i>. 2026;114. doi:<a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">10.1016/j.ffa.2026.102828</a>","mla":"Klawuhn, Lukas-André Dominik, et al. “The Intersection Distribution: New Results and Perspectives.” <i>Finite Fields and Their Applications</i>, vol. 114, 102828, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.ffa.2026.102828\">10.1016/j.ffa.2026.102828</a>."},"doi":"10.1016/j.ffa.2026.102828","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S1071579726000390","open_access":"1"}],"article_number":"102828","language":[{"iso":"eng"}],"date_updated":"2026-05-06T15:08:06Z","intvolume":"       114","article_type":"original","title":"The Intersection Distribution: New Results and Perspectives","year":"2026","author":[{"id":"91965","full_name":"Klawuhn, Lukas-André Dominik","orcid":"0009-0009-7736-4885","last_name":"Klawuhn","first_name":"Lukas-André Dominik"},{"first_name":"Sophie","last_name":"Huczynska","full_name":"Huczynska, Sophie"},{"last_name":"Paterson","first_name":"Maura","full_name":"Paterson, Maura"}],"type":"journal_article","department":[{"_id":"100"}],"date_created":"2025-10-08T14:52:20Z","abstract":[{"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. ","lang":"eng"}],"publication":"Finite Fields and Their Applications"},{"oa":"1","citation":{"ieee":"L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings and their designs,” <i>Algebraic Combinatorics</i>, vol. 9, no. 3, pp. 789–809, 2026, doi: <a href=\"https://doi.org/10.5802/alco.490\">10.5802/alco.490</a>.","apa":"Klawuhn, L.-A. D., &#38; Bamberg, J. (2026). On the association scheme of perfect matchings and their designs. <i>Algebraic Combinatorics</i>, <i>9</i>(3), 789–809. <a href=\"https://doi.org/10.5802/alco.490\">https://doi.org/10.5802/alco.490</a>","short":"L.-A.D. Klawuhn, J. Bamberg, Algebraic Combinatorics 9 (2026) 789–809.","chicago":"Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs.” <i>Algebraic Combinatorics</i> 9, no. 3 (2026): 789–809. <a href=\"https://doi.org/10.5802/alco.490\">https://doi.org/10.5802/alco.490</a>.","mla":"Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme of Perfect Matchings and Their Designs.” <i>Algebraic Combinatorics</i>, vol. 9, no. 3, 2026, pp. 789–809, doi:<a href=\"https://doi.org/10.5802/alco.490\">10.5802/alco.490</a>.","bibtex":"@article{Klawuhn_Bamberg_2026, title={On the association scheme of perfect matchings and their designs}, volume={9}, DOI={<a href=\"https://doi.org/10.5802/alco.490\">10.5802/alco.490</a>}, number={3}, journal={Algebraic Combinatorics}, author={Klawuhn, Lukas-André Dominik and Bamberg, John}, year={2026}, pages={789–809} }","ama":"Klawuhn L-AD, Bamberg J. On the association scheme of perfect matchings and their designs. <i>Algebraic Combinatorics</i>. 2026;9(3):789-809. doi:<a href=\"https://doi.org/10.5802/alco.490\">10.5802/alco.490</a>"},"page":"789-809","_id":"60491","user_id":"91965","volume":9,"status":"public","date_created":"2025-07-02T07:37:23Z","type":"journal_article","department":[{"_id":"100"}],"issue":"3","publication":"Algebraic Combinatorics","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"}],"main_file_link":[{"open_access":"1","url":"https://alco.centre-mersenne.org/articles/10.5802/alco.490/"}],"language":[{"iso":"eng"}],"doi":"10.5802/alco.490","title":"On the association scheme of perfect matchings and their designs","year":"2026","author":[{"first_name":"Lukas-André Dominik","last_name":"Klawuhn","orcid":"0009-0009-7736-4885","full_name":"Klawuhn, Lukas-André Dominik","id":"91965"},{"first_name":"John","last_name":"Bamberg","full_name":"Bamberg, John"}],"date_updated":"2026-07-10T12:26:11Z","intvolume":"         9"},{"date_created":"2026-08-17T10:29:36Z","external_id":{"arxiv":["2608.14437"]},"department":[{"_id":"100"}],"type":"preprint","citation":{"short":"M. Kiermaier, L.-A.D. Klawuhn, (2026).","chicago":"Kiermaier, Michael, and Lukas-André Dominik Klawuhn. “Intersection Numbers for Designs in Regular Semilattices,” 2026.","apa":"Kiermaier, M., &#38; Klawuhn, L.-A. D. (2026). <i>Intersection numbers for designs in regular semilattices</i>.","ieee":"M. Kiermaier and L.-A. D. Klawuhn, “Intersection numbers for designs in regular semilattices.” 2026.","ama":"Kiermaier M, Klawuhn L-AD. Intersection numbers for designs in regular semilattices. Published online 2026.","bibtex":"@article{Kiermaier_Klawuhn_2026, title={Intersection numbers for designs in regular semilattices}, author={Kiermaier, Michael and Klawuhn, Lukas-André Dominik}, year={2026} }","mla":"Kiermaier, Michael, and Lukas-André Dominik Klawuhn. <i>Intersection Numbers for Designs in Regular Semilattices</i>. 2026."},"abstract":[{"text":"We generalize intersection numbers for combinatorial designs to designs in finite meet-semilattices satisfying suitable regularity conditions. While designs in regular semilattices go back to Delsarte, our regularity assumptions are weaker than his and need not give rise to an association scheme. In this framework, we extend Mendelsohn's equations, prove a generalized Singleton bound with Steiner systems as equality cases, and determine the block intersection distribution at any block of a Steiner system. In particular, this distribution is independent of the chosen block.\r\n  Specializing to several classical semilattice families, our results recover a number of well-known distributions in coding and design theory. In the Hamming and the $q$-Hamming (or bilinear forms) schemes, they give the local distance distributions of MDS and MRD codes, respectively. In the Johnson and $q$-Johnson (or Graßmann) schemes, they reproduce the block intersection distribution of classical and $q$-analog Steiner systems, equivalently the distance distribution of diameter-perfect constant-weight codes and diameter-perfect constant-dimension subspace codes. For the $q$-Johnson schemes, to the best of our knowledge, this result is new. As a further illustration, we apply our theory to designs of perfect matchings.\r\n  Our approach provides a unified treatment of these cases in the strongest form known in the literature, determining the distribution relative to each individual block or codeword, without averaging and without linearity or additivity assumptions. Moreover, it identifies the natural double-counting objects underlying these distributions, leading to formulas in the regularity parameters of the semilattice and avoiding the more cumbersome expressions that arise in eigenvalue-based approaches via the ambient association scheme.","lang":"eng"}],"_id":"66731","language":[{"iso":"eng"}],"user_id":"91965","author":[{"last_name":"Kiermaier","first_name":"Michael","full_name":"Kiermaier, Michael"},{"last_name":"Klawuhn","orcid":"0009-0009-7736-4885","first_name":"Lukas-André Dominik","full_name":"Klawuhn, Lukas-André Dominik","id":"91965"}],"status":"public","title":"Intersection numbers for designs in regular semilattices","year":"2026","date_updated":"2026-08-17T10:31:03Z"},{"date_created":"2024-01-08T14:39:54Z","department":[{"_id":"100"}],"type":"journal_article","citation":{"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>.","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} }","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>","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>.","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>","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>.","short":"C. Weiß, Des. Codes Cryptogr. 93 (2025) 971–981."},"publication":"Des. Codes Cryptogr.","abstract":[{"lang":"eng","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."}],"_id":"50299","language":[{"iso":"eng"}],"page":"971 - 981","volume":93,"doi":"10.1007/s10623-024-01471-1","user_id":"70420","author":[{"first_name":"Charlene","last_name":"Weiß","full_name":"Weiß, Charlene","id":"70420"}],"title":"Nontrivial $t$-designs in polar spaces exist for all $t$","status":"public","year":"2025","intvolume":"        93","date_updated":"2026-02-25T13:51:50Z","publication_status":"published"},{"user_id":"91965","_id":"63384","language":[{"iso":"eng"}],"date_updated":"2025-12-19T11:23:41Z","title":"Linear dimension of group actions","year":"2025","status":"public","author":[{"first_name":"Alice","last_name":"Devillers","full_name":"Devillers, Alice"},{"full_name":"Giudici, Michael","first_name":"Michael","last_name":"Giudici"},{"last_name":"Hawtin","first_name":"Daniel R.","full_name":"Hawtin, Daniel R."},{"id":"91965","orcid":"0009-0009-7736-4885","first_name":"Lukas-André Dominik","last_name":"Klawuhn","full_name":"Klawuhn, Lukas-André Dominik"},{"full_name":"Morgan, Luke","first_name":"Luke","last_name":"Morgan"}],"type":"preprint","department":[{"_id":"100"}],"external_id":{"arxiv":["2512.16079"]},"date_created":"2025-12-19T11:20:46Z","abstract":[{"lang":"eng","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."}],"citation":{"ama":"Devillers A, Giudici M, Hawtin DR, Klawuhn L-AD, Morgan L. Linear dimension of group actions. Published online 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} }","mla":"Devillers, Alice, et al. <i>Linear Dimension of Group Actions</i>. 2025.","chicago":"Devillers, Alice, Michael Giudici, Daniel R. Hawtin, Lukas-André Dominik Klawuhn, and Luke Morgan. “Linear Dimension of Group Actions,” 2025.","short":"A. Devillers, M. Giudici, D.R. Hawtin, L.-A.D. Klawuhn, L. Morgan, (2025).","apa":"Devillers, A., Giudici, M., Hawtin, D. R., Klawuhn, L.-A. D., &#38; Morgan, L. (2025). <i>Linear dimension of group actions</i>.","ieee":"A. Devillers, M. Giudici, D. R. Hawtin, L.-A. D. Klawuhn, and L. Morgan, “Linear dimension of group actions.” 2025."}},{"doi":"10.1007/s00209-024-03511-x","user_id":"46953","volume":307,"_id":"53534","language":[{"iso":"eng"}],"date_updated":"2024-06-17T10:04:29Z","intvolume":"       307","year":"2024","title":"Transitivity in finite general linear groups","status":"public","author":[{"full_name":"Ernst, Alena","first_name":"Alena","last_name":"Ernst","id":"46953"},{"full_name":"Schmidt, Kai-Uwe","first_name":"Kai-Uwe","last_name":"Schmidt"}],"type":"journal_article","department":[{"_id":"100"}],"date_created":"2024-04-17T12:26:51Z","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"}],"issue":"45","publication":"Mathematische Zeitschrift","citation":{"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>","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>.","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} }","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>"}},{"date_updated":"2024-11-15T12:34:03Z","author":[{"id":"91965","full_name":"Klawuhn, Lukas-André Dominik","orcid":"0009-0009-7736-4885","last_name":"Klawuhn","first_name":"Lukas-André Dominik"},{"full_name":"Schmidt, Kai-Uwe","last_name":"Schmidt","first_name":"Kai-Uwe"}],"status":"public","title":"Transitivity in wreath products with symmetric groups","year":"2024","user_id":"91965","_id":"56429","language":[{"iso":"eng"}],"page":"38","abstract":[{"lang":"eng","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 $S_n$."}],"citation":{"chicago":"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).","ieee":"L.-A. D. Klawuhn and K.-U. Schmidt, “Transitivity in wreath products with symmetric groups,” <i>arXiv:2409.20495</i>. 2024.","apa":"Klawuhn, L.-A. D., &#38; Schmidt, K.-U. (2024). Transitivity in wreath products with symmetric groups. In <i>arXiv:2409.20495</i>.","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} }","ama":"Klawuhn L-AD, Schmidt K-U. Transitivity in wreath products with symmetric groups. <i>arXiv:240920495</i>. Published online 2024.","mla":"Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath Products with Symmetric Groups.” <i>ArXiv:2409.20495</i>, 2024."},"publication":"arXiv:2409.20495","department":[{"_id":"100"}],"type":"preprint","date_created":"2024-10-08T13:14:45Z","external_id":{"arxiv":["2409.20495"]}},{"language":[{"iso":"eng"}],"_id":"50298","volume":3,"user_id":"70420","doi":"10.5070/c63160424","author":[{"last_name":"Schmidt","first_name":"Kai-Uwe","full_name":"Schmidt, Kai-Uwe"},{"full_name":"Weiß, Charlene","last_name":"Weiß","first_name":"Charlene","id":"70420"}],"title":"Packings and Steiner systems in polar spaces","status":"public","year":"2023","intvolume":"         3","publication_status":"published","date_updated":"2024-01-08T14:39:20Z","date_created":"2024-01-08T14:33:54Z","department":[{"_id":"100"}],"type":"journal_article","citation":{"short":"K.-U. Schmidt, C. Weiß, Combinatorial Theory 3 (2023).","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>.","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>.","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} }","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>","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>."},"issue":"1","publication":"Combinatorial Theory","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."}]},{"abstract":[{"lang":"eng","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."}],"issue":"9","publication":"Journal of Combinatorial Designs","department":[{"_id":"100"}],"type":"journal_article","date_created":"2024-01-08T14:25:28Z","intvolume":"        31","date_updated":"2024-01-08T14:38:53Z","publication_status":"published","author":[{"full_name":"Schmidt, Kai‐Uwe","last_name":"Schmidt","first_name":"Kai‐Uwe"},{"id":"70420","full_name":"Weiß, Charlene","last_name":"Weiß","first_name":"Charlene"}],"title":"Existence of small ordered orthogonal arrays","year":"2023","doi":"10.1002/jcd.21903","language":[{"iso":"eng"}],"citation":{"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>.","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>","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} }","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>","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.","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>."},"status":"public","volume":31,"user_id":"70420","_id":"50297","publisher":"Wiley","page":"422-431"},{"citation":{"short":"C. Weiß, Linear Programming Bounds in Classical Association Schemes, 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>.","ieee":"C. Weiß, <i>Linear programming bounds in classical association schemes</i>. 2023.","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>","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>","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>."},"abstract":[{"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.","lang":"eng"}],"date_created":"2024-01-08T14:42:12Z","department":[{"_id":"100"}],"type":"dissertation","author":[{"last_name":"Weiß","first_name":"Charlene","full_name":"Weiß, Charlene","id":"70420"}],"year":"2023","status":"public","title":"Linear programming bounds in classical association schemes","date_updated":"2024-01-08T14:46:14Z","_id":"50300","language":[{"iso":"eng"}],"user_id":"70420","doi":"10.17619/UNIPB/1-1672"},{"date_updated":"2024-05-07T08:29:59Z","publication_status":"published","intvolume":"       175","year":"2023","title":"Intersection theorems for finite general linear groups","author":[{"id":"46953","full_name":"Ernst, Alena","first_name":"Alena","last_name":"Ernst"},{"full_name":"Schmidt, Kai-Uwe","first_name":"Kai-Uwe","last_name":"Schmidt"}],"publication_identifier":{"issn":["0305-0041","1469-8064"]},"doi":"10.1017/s0305004123000075","language":[{"iso":"eng"}],"issue":"1","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","type":"journal_article","keyword":["General Mathematics"],"department":[{"_id":"100"}],"date_created":"2024-04-17T12:23:18Z","status":"public","user_id":"46953","volume":175,"page":"129-160","publisher":"Cambridge University Press (CUP)","_id":"53533","citation":{"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>","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>.","short":"A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 129–160.","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>.","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>.","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>","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} }"}}]