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pro vyhledávání: '"Ceria, Michela"'
We define and study q-delta-matroids, and q-g-matroids. These objects are analogues, for finite-dimensional vector spaces over finite fields, of delta-matroids and g-matroids arising from finite sets. We compare axiomatic descriptions with definition
Externí odkaz:
http://arxiv.org/abs/2406.14944
Autor:
Ceria, Michela, Pavese, Francesco
In $\mathrm{PG}(3, q)$, $q = 2^n$, $n \ge 3$, let ${\cal A} = \{(1,t,t^{2^h},t^{2^h+1}) \mid t \in \mathbb{F}_q\} \cup \{(0,0,0,1)\}$, with $\mathrm{gcd}(n,h) = 1$, be a $(q+1)$-arc and let $G_h \simeq \mathrm{PGL}(2, q)$ be the stabilizer of $\cal A
Externí odkaz:
http://arxiv.org/abs/2208.00503
Autor:
Ceria, Michela, Jurrius, Relinde
Publikováno v:
Advances in Applied Mathematics, Volume 153, February 2024, 102632
It is well known that in q-matroids, axioms for independent spaces, bases, and spanning spaces differ from the classical case of matroids, since the straightforward q-analogue of the classical axioms does not give a q-matroid. For this reason, a four
Externí odkaz:
http://arxiv.org/abs/2207.07324
Autor:
Ceria, Michela, Pavese, Francesco
In this paper we are concerned with $m$-ovoids of the symplectic polar space ${\cal W}(2n+1, q)$, $q$ even. In particular we show the existence of an elliptic quadric of ${\rm PG}(2n+1, q)$ not polarizing to ${\cal W}(2n+1, q)$ forming a $\left(\frac
Externí odkaz:
http://arxiv.org/abs/2207.01128
In this paper we provide constructive lower bounds on the sizes of the largest partial ovoids of the symplectic polar spaces ${\cal W}(3, q)$, $q$ odd square, $q \not\equiv 0 \pmod{3}$, ${\cal W}(5, q)$ and of the Hermitian polar spaces ${\cal H}(4,
Externí odkaz:
http://arxiv.org/abs/2203.04553
The solving degree of a system of multivariate polynomial equations provides an upper bound for the complexity of computing the solutions of the system via Groebner bases methods. In this paper, we consider polynomial systems that are obtained via We
Externí odkaz:
http://arxiv.org/abs/2112.10506
Autor:
Ceria, Michela, Jurrius, Relinde
For classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for $q$-matroids, the $q$-analogue of matroids. This is a lot less straightforward than in t
Externí odkaz:
http://arxiv.org/abs/2109.13637
Several classes of near-MDS codes of ${\rm PG}(3,q)$ are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of a symplectic polar space ${\cal W}(3, q)$ or starting from the $q+1$
Externí odkaz:
http://arxiv.org/abs/2106.03402
Publikováno v:
Designs, Codes and Cryptography (2022) 90:1503-1519
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult. Here we inve
Externí odkaz:
http://arxiv.org/abs/2105.14508
The Assmus-Mattson theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs. In this work we present a further two-fold generalisation: first from matroids to polymatroids and also f
Externí odkaz:
http://arxiv.org/abs/2104.12463