Zobrazeno 1 - 10
of 81
pro vyhledávání: '"Podesta, Ricardo"'
Autor:
Podestá, Ricardo A., Videla, Denis E.
In this work we consider the class of Cayley graphs known as generalized Paley graphs (GP-graphs for short) given by $\Gamma(k,q) = Cay(\mathbb{F}_q, \{x^k : x\in \mathbb{F}_q^* \})$, where $\mathbb{F}_q$ is a finite field with $q$ elements, both in
Externí odkaz:
http://arxiv.org/abs/2410.00281
In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field $\mathbb{F}_q$ with $q$ elements. Given a finite separable extension $\mathcal{M}/\mathcal{F}$ of function fields and an iso-dual AG-code
Externí odkaz:
http://arxiv.org/abs/2311.08992
Autor:
Podestá, Ricardo A., Videla, Denis E.
We study the spectrum of generalized Paley graphs $\Gamma(k,q)=Cay(\mathbb{F}_q,R_k)$, undirected or not, with $R_k=\{x^k:x\in \mathbb{F}_q^*\}$ where $q=p^m$ with $p$ prime and $k\mid q-1$. We first show that the eigenvalues of $\Gamma(k,q)$ are giv
Externí odkaz:
http://arxiv.org/abs/2310.15378
Autor:
Podestá, Ricardo A., Videla, Denis E.
In this paper we study Waring numbers $g_R(k)$ for $(R,\frak m)$ a finite commutative local ring with identity and $k \in \mathbb{N}$ with $(k,|R|)=1$. We first relate the Waring number $g_R(k)$ with the diameter of the Cayley graphs $G_R(k)=Cay(R,U_
Externí odkaz:
http://arxiv.org/abs/2212.12396
In this work we consider interval metrics on groups; that is, integral invariant metrics whose associated weight functions do not have gaps. We give conditions for a group to have and to have not interval metrics. Then we study Lee metrics on general
Externí odkaz:
http://arxiv.org/abs/2206.04555
Autor:
Podestá, Ricardo A., Videla, Denis E.
We consider generalized Paley graphs $\Gamma(k,q)$, generalized Paley sum graphs $\Gamma^+(k,q)$, and their corresponding complements $\bar \Gamma(k,q)$ and $\bar \Gamma^+(k,q)$, for $k=3,4$. Denote by $\Gamma = \Gamma^*(k,q)$ either $\Gamma(k,q)$ or
Externí odkaz:
http://arxiv.org/abs/2204.08509
We study invariant and bi-invariant metrics on groups focusing on finite groups $G$. We show that non-equivalent (bi) invariant metrics on $G$ are in 1-1 correspondence with unitary symmetric (conjugate) partitions on $G$. To every metric group $(G,d
Externí odkaz:
http://arxiv.org/abs/2112.15049
In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms. We prove th
Externí odkaz:
http://arxiv.org/abs/2106.08884
Autor:
Podestá, Ricardo A., Videla, Denis E.
We give necessary and sufficient conditions on the parameters of a regular graph $\Gamma$ (with or without loops) such that $E(\Gamma)=E(\overline \Gamma)$. We study complementary equienergetic cubic graphs obtaining classifications up to isomorphism
Externí odkaz:
http://arxiv.org/abs/2010.06378
Autor:
Podestá, Ricardo A., Videla, Denis E.
We prove that the Cayley graphs $X(G,S)$ and $X^+(G,S)$ are equienergetic for any abelian group $G$ and any symmetric subset $S$. We then focus on the family of unitary Cayley graphs $G_R=X(R,R^*)$, where $R$ is a finite commutative ring with identit
Externí odkaz:
http://arxiv.org/abs/2007.01300