Denis E. Videla

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20192022

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6 papers · 1 filter

math.CO2022

Generalized Paley graphs equienergetic with their complements

Ricardo A. Podestá, Denis E. Videla

We consider generalized Paley graphs $Γ (k, q)$ , generalized Paley sum graphs $Γ^{+} (k, q)$ , and their corresponding complements $Γ ˉ (k, q)$ and $Γ ˉ^{+} (k, q)$ , for $k = 3, 4$ . Denote b…

math.CO2020

Integral equienergetic non-isospectral unitary Cayley graphs

Ricardo A. Podestá, Denis E. Videla

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 grap…

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.CO2019

Spectral properties of generalized Paley graphs and their associated irreducible cyclic codes

Ricardo A. Podestá, Denis E. Videla

For $q = p^{m}$ with $p$ prime and $k ∣ q - 1$ , we consider the generalized Paley graph $Γ (k, q) = C a y (F_{q}, R_{k})$ , with $R_{k} = {x^{k} : x \in F_{q}^{*}}$ , and the irreduci…

math.CO2019

On diagonal equations over finite fields via walks in NEPS of graphs

Denis E. Videla

In this paper, we obtain an explicit combinatorial formula for the number of solutions $(x_{1}, \dots, x_{r}) \in F_{p^{ab}}$ to the diagonal equation $x_{1}^{k} + \dots + x_{r}^{k} = α$ …

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…