---
_id: '50299'
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."
author:
- first_name: Charlene
  full_name: Weiß, Charlene
  id: '70420'
  last_name: Weiß
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>
  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>
  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}
    }'
  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>.'
  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>.'
  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>.
  short: C. Weiß, Des. Codes Cryptogr. 93 (2025) 971–981.
date_created: 2024-01-08T14:39:54Z
date_updated: 2026-02-25T13:51:50Z
department:
- _id: '100'
doi: 10.1007/s10623-024-01471-1
intvolume: '        93'
language:
- iso: eng
page: 971 - 981
publication: Des. Codes Cryptogr.
publication_status: published
status: public
title: Nontrivial $t$-designs in polar spaces exist for all $t$
type: journal_article
user_id: '70420'
volume: 93
year: '2025'
...
---
_id: '50298'
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.
author:
- first_name: Kai-Uwe
  full_name: Schmidt, Kai-Uwe
  last_name: Schmidt
- first_name: Charlene
  full_name: Weiß, Charlene
  id: '70420'
  last_name: Weiß
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>
  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} }'
  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>.'
  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).
date_created: 2024-01-08T14:33:54Z
date_updated: 2024-01-08T14:39:20Z
department:
- _id: '100'
doi: 10.5070/c63160424
intvolume: '         3'
issue: '1'
language:
- iso: eng
publication: Combinatorial Theory
publication_status: published
status: public
title: Packings and Steiner systems in polar spaces
type: journal_article
user_id: '70420'
volume: 3
year: '2023'
...
---
_id: '50297'
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.
author:
- first_name: Kai‐Uwe
  full_name: Schmidt, Kai‐Uwe
  last_name: Schmidt
- first_name: Charlene
  full_name: Weiß, Charlene
  id: '70420'
  last_name: Weiß
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>
  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} }'
  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>.'
  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>.
  short: K. Schmidt, C. Weiß, Journal of Combinatorial Designs 31 (2023) 422–431.
date_created: 2024-01-08T14:25:28Z
date_updated: 2024-01-08T14:38:53Z
department:
- _id: '100'
doi: 10.1002/jcd.21903
intvolume: '        31'
issue: '9'
language:
- iso: eng
page: 422-431
publication: Journal of Combinatorial Designs
publication_status: published
publisher: Wiley
status: public
title: Existence of small ordered orthogonal arrays
type: journal_article
user_id: '70420'
volume: 31
year: '2023'
...
---
_id: '50300'
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.
author:
- first_name: Charlene
  full_name: Weiß, Charlene
  id: '70420'
  last_name: Weiß
citation:
  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>
  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} }'
  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.
  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.
date_created: 2024-01-08T14:42:12Z
date_updated: 2024-01-08T14:46:14Z
department:
- _id: '100'
doi: 10.17619/UNIPB/1-1672
language:
- iso: eng
status: public
title: Linear programming bounds in classical association schemes
type: dissertation
user_id: '70420'
year: '2023'
...
---
_id: '52127'
abstract:
- lang: eng
  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.
author:
- first_name: Lucia
  full_name: Moura, Lucia
  last_name: Moura
- first_name: Anamari
  full_name: Nakic, Anamari
  last_name: Nakic
- first_name: Patric
  full_name: Östergård, Patric
  last_name: Östergård
- first_name: Alfred
  full_name: Wassermann, Alfred
  last_name: Wassermann
- first_name: Charlene
  full_name: Weiß, Charlene
  id: '70420'
  last_name: Weiß
citation:
  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>
  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>
  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} }'
  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>.
  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.
  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>.
  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.
date_created: 2024-02-27T15:44:41Z
date_updated: 2024-02-27T15:48:12Z
doi: 10.4230/DagRep.13.4.40
keyword:
- automorphism groups
- combinatorial algorithms
- finite geometries
- subspace designs
language:
- iso: eng
page: 40-57
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
series_title: Dagstuhl Reports
status: public
title: Pushing the Limits of Computational Combinatorial Constructions (Dagstuhl Seminar
  23161)
type: report
user_id: '70420'
volume: 13, Issue 4
year: '2023'
...