---
_id: '61759'
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. '
article_number: '102828'
article_type: original
author:
- first_name: Lukas-André Dominik
  full_name: Klawuhn, Lukas-André Dominik
  id: '91965'
  last_name: Klawuhn
  orcid: 0009-0009-7736-4885
- first_name: Sophie
  full_name: Huczynska, Sophie
  last_name: Huczynska
- first_name: Maura
  full_name: Paterson, Maura
  last_name: Paterson
citation:
  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>'
  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} }'
  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>.'
  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>.'
  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>.'
  short: L.-A.D. Klawuhn, S. Huczynska, M. Paterson, Finite Fields and Their Applications
    114 (2026).
date_created: 2025-10-08T14:52:20Z
date_updated: 2026-05-06T15:08:06Z
department:
- _id: '100'
doi: 10.1016/j.ffa.2026.102828
intvolume: '       114'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.sciencedirect.com/science/article/pii/S1071579726000390
oa: '1'
publication: Finite Fields and Their Applications
publisher: Elsevier
status: public
title: 'The Intersection Distribution: New Results and Perspectives'
type: journal_article
user_id: '91965'
volume: 114
year: '2026'
...
---
_id: '60491'
abstract:
- lang: eng
  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 $S_{2n}$.
author:
- first_name: Lukas-André Dominik
  full_name: Klawuhn, Lukas-André Dominik
  id: '91965'
  last_name: Klawuhn
  orcid: 0009-0009-7736-4885
- first_name: John
  full_name: Bamberg, John
  last_name: Bamberg
citation:
  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>
  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>
  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} }'
  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>.'
  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>.'
  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>.
  short: L.-A.D. Klawuhn, J. Bamberg, Algebraic Combinatorics 9 (2026) 789–809.
date_created: 2025-07-02T07:37:23Z
date_updated: 2026-07-10T12:26:11Z
department:
- _id: '100'
doi: 10.5802/alco.490
intvolume: '         9'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://alco.centre-mersenne.org/articles/10.5802/alco.490/
oa: '1'
page: 789-809
publication: Algebraic Combinatorics
status: public
title: On the association scheme of perfect matchings and their designs
type: journal_article
user_id: '91965'
volume: 9
year: '2026'
...
---
_id: '66731'
abstract:
- lang: eng
  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."
author:
- first_name: Michael
  full_name: Kiermaier, Michael
  last_name: Kiermaier
- first_name: Lukas-André Dominik
  full_name: Klawuhn, Lukas-André Dominik
  id: '91965'
  last_name: Klawuhn
  orcid: 0009-0009-7736-4885
citation:
  ama: Kiermaier M, Klawuhn L-AD. Intersection numbers for designs in regular semilattices.
    Published online 2026.
  apa: Kiermaier, M., &#38; Klawuhn, L.-A. D. (2026). <i>Intersection numbers for
    designs in regular semilattices</i>.
  bibtex: '@article{Kiermaier_Klawuhn_2026, title={Intersection numbers for designs
    in regular semilattices}, author={Kiermaier, Michael and Klawuhn, Lukas-André
    Dominik}, year={2026} }'
  chicago: Kiermaier, Michael, and Lukas-André Dominik Klawuhn. “Intersection Numbers
    for Designs in Regular Semilattices,” 2026.
  ieee: M. Kiermaier and L.-A. D. Klawuhn, “Intersection numbers for designs in regular
    semilattices.” 2026.
  mla: Kiermaier, Michael, and Lukas-André Dominik Klawuhn. <i>Intersection Numbers
    for Designs in Regular Semilattices</i>. 2026.
  short: M. Kiermaier, L.-A.D. Klawuhn, (2026).
date_created: 2026-08-17T10:29:36Z
date_updated: 2026-08-17T10:31:03Z
department:
- _id: '100'
external_id:
  arxiv:
  - '2608.14437'
language:
- iso: eng
status: public
title: Intersection numbers for designs in regular semilattices
type: preprint
user_id: '91965'
year: '2026'
...
---
_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: '63384'
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."
author:
- first_name: Alice
  full_name: Devillers, Alice
  last_name: Devillers
- first_name: Michael
  full_name: Giudici, Michael
  last_name: Giudici
- first_name: Daniel R.
  full_name: Hawtin, Daniel R.
  last_name: Hawtin
- first_name: Lukas-André Dominik
  full_name: Klawuhn, Lukas-André Dominik
  id: '91965'
  last_name: Klawuhn
  orcid: 0009-0009-7736-4885
- first_name: Luke
  full_name: Morgan, Luke
  last_name: Morgan
citation:
  ama: Devillers A, Giudici M, Hawtin DR, Klawuhn L-AD, Morgan L. Linear dimension
    of group actions. Published online 2025.
  apa: Devillers, A., Giudici, M., Hawtin, D. R., Klawuhn, L.-A. D., &#38; Morgan,
    L. (2025). <i>Linear dimension of group actions</i>.
  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} }'
  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).
date_created: 2025-12-19T11:20:46Z
date_updated: 2025-12-19T11:23:41Z
department:
- _id: '100'
external_id:
  arxiv:
  - '2512.16079'
language:
- iso: eng
status: public
title: Linear dimension of group actions
type: preprint
user_id: '91965'
year: '2025'
...
---
_id: '53534'
abstract:
- lang: eng
  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."
author:
- first_name: Alena
  full_name: Ernst, Alena
  id: '46953'
  last_name: Ernst
- first_name: Kai-Uwe
  full_name: Schmidt, Kai-Uwe
  last_name: Schmidt
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>
  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>
  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} }'
  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>.'
  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>.
  short: A. Ernst, K.-U. Schmidt, Mathematische Zeitschrift 307 (2024).
date_created: 2024-04-17T12:26:51Z
date_updated: 2024-06-17T10:04:29Z
department:
- _id: '100'
doi: 10.1007/s00209-024-03511-x
intvolume: '       307'
issue: '45'
language:
- iso: eng
publication: Mathematische Zeitschrift
status: public
title: Transitivity in finite general linear groups
type: journal_article
user_id: '46953'
volume: 307
year: '2024'
...
---
_id: '56429'
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 $S_n$."
author:
- first_name: Lukas-André Dominik
  full_name: Klawuhn, Lukas-André Dominik
  id: '91965'
  last_name: Klawuhn
  orcid: 0009-0009-7736-4885
- first_name: Kai-Uwe
  full_name: Schmidt, Kai-Uwe
  last_name: Schmidt
citation:
  ama: Klawuhn L-AD, Schmidt K-U. Transitivity in wreath products with symmetric groups.
    <i>arXiv:240920495</i>. Published online 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} }'
  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).
date_created: 2024-10-08T13:14:45Z
date_updated: 2024-11-15T12:34:03Z
department:
- _id: '100'
external_id:
  arxiv:
  - '2409.20495'
language:
- iso: eng
page: '38'
publication: arXiv:2409.20495
status: public
title: Transitivity in wreath products with symmetric groups
type: preprint
user_id: '91965'
year: '2024'
...
---
_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: '53533'
author:
- first_name: Alena
  full_name: Ernst, Alena
  id: '46953'
  last_name: Ernst
- first_name: Kai-Uwe
  full_name: Schmidt, Kai-Uwe
  last_name: Schmidt
citation:
  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>
  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>
  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} }'
  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>.'
  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>.'
  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>.
  short: A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical
    Society 175 (2023) 129–160.
date_created: 2024-04-17T12:23:18Z
date_updated: 2024-05-07T08:29:59Z
department:
- _id: '100'
doi: 10.1017/s0305004123000075
intvolume: '       175'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 129-160
publication: Mathematical Proceedings of the Cambridge Philosophical Society
publication_identifier:
  issn:
  - 0305-0041
  - 1469-8064
publication_status: published
publisher: Cambridge University Press (CUP)
status: public
title: Intersection theorems for finite general linear groups
type: journal_article
user_id: '46953'
volume: 175
year: '2023'
...