Zobrazeno 1 - 10
of 144
pro vyhledávání: '"Micheli, Giacomo"'
We introduce a new technique to construct rank-metric codes using the arithmetic theory of Drinfeld modules over global fields, and Dirichlet Theorem on polynomial arithmetic progressions. Using our methods, we obtain a new infinite family of optimal
Externí odkaz:
http://arxiv.org/abs/2407.06081
Autor:
Goksel, Vefa, Micheli, Giacomo
Let $q$ be an odd prime power. Let $f\in \mathbb{F}_q[x]$ be a polynomial having degree at least $2$, $a\in \mathbb{F}_q$, and denote by $f^n$ the $n$-th iteration of $f$. Let $\chi$ be the quadratic character of $\mathbb{F}_q$, and $\mathcal{O}_f(a)
Externí odkaz:
http://arxiv.org/abs/2403.19642
Autor:
Cherubini, Giacomo, Micheli, Giacomo
Let $n$ be a prime power, $r$ be a prime with $r\mid n-1$, and $\varepsilon\in (0,1/2)$. Using the theory of multiplicative character sums and superelliptic curves, we construct new codes over $\mathbb F_r$ having length $n$, relative distance $(r-1)
Externí odkaz:
http://arxiv.org/abs/2401.07986
In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic number fiel
Externí odkaz:
http://arxiv.org/abs/2304.09071
Autor:
Bastioni, Luca, Micheli, Giacomo
Let $m$ be a positive integer and $q$ be a prime power. For large finite base fields $\mathbb F_q$, we show that any curve can be used to produce a complete $m$-arc as long as some generic explicit geometric conditions on the curve are verified. To s
Externí odkaz:
http://arxiv.org/abs/2303.13670
Differential cryptanalysis famously uses statistical biases in the propagation of differences in a block cipher to attack the cipher. In this paper, we investigate the existence of more general statistical biases in the differences. To this end, we d
Externí odkaz:
http://arxiv.org/abs/2208.03884
In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that allows to give
Externí odkaz:
http://arxiv.org/abs/2207.10383
The local to global principle for densities is a very convenient tool proposed by Poonen and Stoll to compute the density of a given subset of the integers. In this paper we provide an effective criterion to find all higher moments of the density (e.
Externí odkaz:
http://arxiv.org/abs/2201.03751
Good polynomials are the fundamental objects in the Tamo-Barg constructions of Locally Recoverable Codes (LRC). In this paper we classify all good polynomials up to degree $5$, providing explicit bounds on the maximal number $\ell$ of sets of size $r
Externí odkaz:
http://arxiv.org/abs/2104.01434
In this paper we prove that the property of being scattered for a $\mathbb{F}_q$-linearized polynomial of small $q$-degree over a finite field $\mathbb{F}_{q^n}$ is unstable, in the sense that, whenever the corresponding linear set has at least one p
Externí odkaz:
http://arxiv.org/abs/2012.15357