R. Podest'a

collaborators

5 papers

math.GM2020

A geometric proof that $3$ , $5$ and $7$ are irrational

Ricardo A. Podestá

We show geometrically that $n$ is irrational for $n = 3, 5, 7$ by adapting Tennenbaum's geometric proof that $2$ is irrational. We also show that this method cannot be used…

math.CO2020

Isometries between finite groups

Ricardo A. Podestá, Maximiliano G. Vides

We prove that if $H$ is a subgroup of index $n$ of any cyclic group $G$ , then $G$ can be isometrically embedded in $(H^{n}, d_{_{H am}}^{n})$ , thus generalizing previous results of Carl…

math.CO2019

The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs

Ricardo A. Podestá, Denis E. Videla

We use known characterizations of generalized Paley graphs which are cartesian decomposable to explicitly compute the spectra of the corresponding associated irreducible cyclic cod…

math.NT2019

The Waring's problem over finite fields through generalized Paley graphs

Ricardo A. Podestá, Denis E. Videla

We show that the Waring's number over a finite field $F_{q}$ , denoted $g (k, q)$ , when exists, coincides with the diameter of the generalized Paley graph $Γ(k,q)=Cay(\mathbb{F…

math.CO2019

Weight distribution of cyclic codes defined by quadratic forms and related curves

Ricardo A. Podestá, Denis E. Videla

We consider cyclic codes $C_{L}$ associated to quadratic trace forms in $m$ variables $Q_{R} (x) = Tr_{q^{m} / q} (x R (x))$ determined by a family $\mathcal…

A geometric proof that 3​, 5​ and 7​ are irrational

Isometries between finite groups

The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs

The Waring's problem over finite fields through generalized Paley graphs

Weight distribution of cyclic codes defined by quadratic forms and related curves

A geometric proof that $3$ , $5$ and $7$ are irrational