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pro vyhledávání: '"Storme, Leo"'
We characterise the minimum weight codewords of the $p$-ary linear code of intersecting lines in ${\rm PG}(3,q)$, $q=p^h$, $q\geq19$, $p$ prime, $h\geq 1$. If $q$ is even, the minimum weight equals $q^3+q^2+q+1$. If $q$ is odd, the minimum weight equ
Externí odkaz:
http://arxiv.org/abs/2403.07451
This paper focuses on non-existence results for Cameron-Liebler $k$-sets. A Cameron-Liebler $k$-set is a collection of $k$-spaces in $\mathrm{PG}(n,q)$ or $\mathrm{AG}(n,q)$ admitting a certain parameter $x$, which is dependent on the size of this co
Externí odkaz:
http://arxiv.org/abs/2403.00519
Publikováno v:
Designs, Codes and Cryptography, 2022
In this article we generalize the concepts that were used in the PhD thesis of Drudge to classify Cameron-Liebler line classes in PG$(n,q), n\geq 3$, to Cameron-Liebler sets of $k$-spaces in PG$(n,q)$ and AG$(n,q)$. In his PhD thesis, Drudge proved t
Externí odkaz:
http://arxiv.org/abs/2106.05684
In this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a {\it junta}; i.e. a subspace code in which all codewords go through
Externí odkaz:
http://arxiv.org/abs/2009.06792
In this paper, we analyze the structure of maximal sets of $k$-dimensional spaces in $\mathrm{PG}(n,q)$ pairwise intersecting in at least a $(k-2)$-dimensional space, for $3 \leq k\leq n-2$. We give an overview of the largest examples of these sets w
Externí odkaz:
http://arxiv.org/abs/2005.05494
Publikováno v:
Electronic journal of Combinatorics, 28(4):11, 2021
We study Cameron-Liebler $k$-sets in the affine geometry, so sets of $k$-spaces in $\text{AG}(n, q)$. This generalizes research on Cameron-Liebler $k$-sets in the projective geometry $\text{PG}(n, q)$. Note that in algebraic combinatorics, Cameron-Li
Externí odkaz:
http://arxiv.org/abs/2003.12429
Publikováno v:
Finite Fields and Their Applications, Volume 67, 2020, 101706, ISSN 1071-5797
The study of Cameron-Liebler line classes in PG($3,q$) arose from classifying specific collineation subgroups of PG($3,q$). Recently, these line classes were considered in new settings. In this point of view, we will generalize the concept of Cameron
Externí odkaz:
http://arxiv.org/abs/2002.02700
Akademický článek
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Publikováno v:
Des. Codes Cryptogr. 88 (4), 771-788 (2020)
Let $C_{n-1}(n,q)$ be the code arising from the incidence of points and hyperplanes in the Desarguesian projective space PG($n,q$). Recently, Polverino and Zullo proved that within this code, all non-zero code words of weight at most $2q^{n-1}$ are s
Externí odkaz:
http://arxiv.org/abs/1905.04978
We investigate subspace codes whose codewords are subspaces of ${\rm PG}(4,q)$ having non-constant dimension. In particular, examples of optimal mixed-dimension subspace codes are provided, showing that ${\cal A}_q(5,3) = 2(q^3+1)$.
Externí odkaz:
http://arxiv.org/abs/1802.09793