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pro vyhledávání: '"Bartoli, Daniele"'
In this note we show (for a large enough dimension of the underlying field) a conjecture of [C. Beierle, C. Carlet, G. Leander, L. Perrin, {\em A further study of quadratic APN permutations in dimension nine}, Finite Fields Appl. 81 (2022), 102049] o
Externí odkaz:
http://arxiv.org/abs/2410.23097
In this paper we use algebraic curves and other algebraic number theory methods to show the validity of a permutation polynomial conjecture regarding $f(X)=X^{q(p-1)+1} +\alpha X^{pq}+X^{q+p-1}$, on finite fields $\mathbb{F}_{q^2}, q=p^k$, from [A. R
Externí odkaz:
http://arxiv.org/abs/2410.22692
The exploration of linear subspaces, particularly scattered subspaces, has garnered considerable attention across diverse mathematical disciplines in recent years, notably within finite geometries and coding theory. Scattered subspaces play a pivotal
Externí odkaz:
http://arxiv.org/abs/2405.09123
Autor:
Bartoli, Daniele, Ghiandoni, Francesco
In this work we present results on the classification of $\mathbb{F}_{q^n}$-linear MRD codes of dimension three. In particular, using connections with certain algebraic varieties over finite fields, we provide non-existence results for MRD codes $\ma
Externí odkaz:
http://arxiv.org/abs/2403.01887
Scattered subspaces and $h$-scattered subspaces have been extensively studied in recent decades for both theoretical purposes and their connections to various applications. While numerous constructions of scattered subspaces exist, relatively few are
Externí odkaz:
http://arxiv.org/abs/2403.01506
Ovoids of the Klein quadric $Q^+(5,q)$ of $\mathrm{PG}(5,q)$ have been studied in the last 40 year, also because of their connection with spreads of $\mathrm{PG}(3,q)$ and hence translation planes. Beside the classical example given by a three dimens
Externí odkaz:
http://arxiv.org/abs/2310.18470
In recent years, several families of scattered polynomials have been investigated in the literature. However, most of them only exist in odd characteristic. In [B. Csajb\'ok, G. Marino and F. Zullo: New maximum scattered linear sets of the projective
Externí odkaz:
http://arxiv.org/abs/2307.12829
Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this paper, we
Externí odkaz:
http://arxiv.org/abs/2306.17081
Autor:
Bartoli, Daniele, Ghiandoni, Francesco
Necessary and sufficient conditions on $A,B\in \mathbb{F}_{q^3}^*$ for $f(X)=X^{q^2-q+1}+AX^{q^2}+BX$ being a permutation polynomial of $\mathbb{F}_{q^3}$ are investigated via a connection with algebraic varieties over finite fields.
Externí odkaz:
http://arxiv.org/abs/2306.09972
Autor:
Bartoli, Daniele, Giannoni, Alessandro
Scattered sequences are a generalization of scattered polynomials. So far, only scattered sequences of order one and two have been constructed. In this paper an infinite family of scattered sequences of order three is obtained. Equivalence issues are
Externí odkaz:
http://arxiv.org/abs/2306.03448