[{"title":"Nontrivial $t$-designs in polar spaces exist for all $t$","doi":"10.1007/s10623-024-01471-1","date_updated":"2026-02-25T13:51:50Z","date_created":"2024-01-08T14:39:54Z","author":[{"last_name":"Weiß","id":"70420","full_name":"Weiß, Charlene","first_name":"Charlene"}],"volume":93,"year":"2025","citation":{"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>.","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.","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>"},"intvolume":"        93","page":"971 - 981","publication_status":"published","language":[{"iso":"eng"}],"_id":"50299","user_id":"70420","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"}],"status":"public","type":"journal_article","publication":"Des. Codes Cryptogr."},{"abstract":[{"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.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Combinatorial Theory","language":[{"iso":"eng"}],"_id":"50298","user_id":"70420","department":[{"_id":"100"}],"year":"2023","citation":{"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).","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>","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>."},"intvolume":"         3","publication_status":"published","issue":"1","title":"Packings and Steiner systems in polar spaces","doi":"10.5070/c63160424","date_updated":"2024-01-08T14:39:20Z","author":[{"full_name":"Schmidt, Kai-Uwe","last_name":"Schmidt","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},{"department":[{"_id":"100"}],"user_id":"70420","_id":"50297","language":[{"iso":"eng"}],"publication":"Journal of Combinatorial Designs","type":"journal_article","status":"public","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."}],"volume":31,"author":[{"first_name":"Kai‐Uwe","full_name":"Schmidt, Kai‐Uwe","last_name":"Schmidt"},{"id":"70420","full_name":"Weiß, Charlene","last_name":"Weiß","first_name":"Charlene"}],"date_created":"2024-01-08T14:25:28Z","date_updated":"2024-01-08T14:38:53Z","publisher":"Wiley","doi":"10.1002/jcd.21903","title":"Existence of small ordered orthogonal arrays","issue":"9","publication_status":"published","page":"422-431","intvolume":"        31","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>","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>.","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>.","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>","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} }","short":"K. Schmidt, C. Weiß, Journal of Combinatorial Designs 31 (2023) 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>."},"year":"2023"},{"citation":{"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>.","short":"C. Weiß, Linear Programming Bounds in Classical Association Schemes, 2023.","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} }","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>","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.","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>"},"year":"2023","author":[{"first_name":"Charlene","id":"70420","full_name":"Weiß, Charlene","last_name":"Weiß"}],"date_created":"2024-01-08T14:42:12Z","date_updated":"2024-01-08T14:46:14Z","doi":"10.17619/UNIPB/1-1672","title":"Linear programming bounds in classical association schemes","type":"dissertation","status":"public","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"}],"user_id":"70420","department":[{"_id":"100"}],"_id":"50300","language":[{"iso":"eng"}]},{"year":"2023","citation":{"short":"L. Moura, A. Nakic, P. Östergård, A. Wassermann, C. Weiß, Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar 23161), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","bibtex":"@book{Moura_Nakic_Östergård_Wassermann_Weiß_2023, series={Dagstuhl Reports}, title={Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar 23161)}, volume={13, Issue 4}, DOI={<a href=\"https://doi.org/10.4230/DagRep.13.4.40\">10.4230/DagRep.13.4.40</a>}, publisher={Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, author={Moura, Lucia and Nakic, Anamari and Östergård, Patric and Wassermann, Alfred and Weiß, Charlene}, year={2023}, pages={40–57}, collection={Dagstuhl Reports} }","mla":"Moura, Lucia, et al. <i>Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar 23161)</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, pp. 40–57, doi:<a href=\"https://doi.org/10.4230/DagRep.13.4.40\">10.4230/DagRep.13.4.40</a>.","apa":"Moura, L., Nakic, A., Östergård, P., Wassermann, A., &#38; Weiß, C. (2023). <i>Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar 23161)</i> (Vols. 13, Issue 4, pp. 40–57). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/DagRep.13.4.40\">https://doi.org/10.4230/DagRep.13.4.40</a>","ieee":"L. Moura, A. Nakic, P. Östergård, A. Wassermann, and C. Weiß, <i>Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar 23161)</i>, vol. 13, Issue 4. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, pp. 40–57.","chicago":"Moura, Lucia, Anamari Nakic, Patric Östergård, Alfred Wassermann, and Charlene Weiß. <i>Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar 23161)</i>. Vol. 13, Issue 4. Dagstuhl Reports. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. <a href=\"https://doi.org/10.4230/DagRep.13.4.40\">https://doi.org/10.4230/DagRep.13.4.40</a>.","ama":"Moura L, Nakic A, Östergård P, Wassermann A, Weiß C. <i>Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar 23161)</i>. Vol 13, Issue 4. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023:40-57. doi:<a href=\"https://doi.org/10.4230/DagRep.13.4.40\">10.4230/DagRep.13.4.40</a>"},"page":"40-57","title":"Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar 23161)","doi":"10.4230/DagRep.13.4.40","date_updated":"2024-02-27T15:48:12Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"first_name":"Lucia","last_name":"Moura","full_name":"Moura, Lucia"},{"last_name":"Nakic","full_name":"Nakic, Anamari","first_name":"Anamari"},{"first_name":"Patric","last_name":"Östergård","full_name":"Östergård, Patric"},{"full_name":"Wassermann, Alfred","last_name":"Wassermann","first_name":"Alfred"},{"first_name":"Charlene","last_name":"Weiß","full_name":"Weiß, Charlene","id":"70420"}],"date_created":"2024-02-27T15:44:41Z","volume":"13, Issue 4","abstract":[{"text":"This report documents the program and the outcomes of Dagstuhl Seminar 23161 \"Pushing the Limits of Computational Combinatorial Constructions\". In this Dagstuhl Seminar, we focused on computational methods for challenging problems in combinatorial construction. This includes algorithms for construction of combinatorial objects with prescribed symmetry, for isomorph-free exhaustive generation, and for combinatorial search. Examples of specific algorithmic techniques are tactical decomposition, the Kramer-Mesner method, algebraic methods, graph isomorphism software, isomorph-free generation, clique-finding methods, heuristic search, SAT solvers, and combinatorial optimization. There was an emphasis on problems involving graphs, designs and codes, also including topics in related fields such as finite geometry, graph decomposition, Hadamard matrices, Latin squares, and q-analogs of designs and codes.","lang":"eng"}],"status":"public","type":"report","keyword":["automorphism groups","combinatorial algorithms","finite geometries","subspace designs"],"language":[{"iso":"eng"}],"_id":"52127","series_title":"Dagstuhl Reports","user_id":"70420"}]