R. Podest'a

activity

20142026

most citedNew identities for binary Krawtchouk polynomials, binomial coefficients and Catalan numbers

1 citations · 1 across the 6 of their papers we have counts for

collaborators

13 papers

cs.IT2026

The weight enumerators of irreducible cyclic codes of length $2^{ℓ}$

Ricardo A. Podestá, Denis E. Videla

Using the spectral relation between irreducible cyclic codes (ICC) and generalized Paley (GP) graphs recently found by the authors, we study the weight distribution of irreducible…

cs.IT2026

The spectral relation between irreducible cyclic codes and generalized Paley graphs

Ricardo A. Podestá, Denis E. Videla

Let $p$ be a prime and $F_{q} / F_{r}$ a finite field extension with $q = p^{m}$ and $r = p^{s}$ . For any $k ∣ q - 1$ , we consider $r$ -ary irreducible cyclic codes (ICC) of the…

math.CO2020

On regular graphs equienergetic with their complements

Ricardo A. Podestá, Denis E. Videla

We give necessary and sufficient conditions on the parameters of a regular graph $Γ$ (with or without loops) such that $E (Γ) = E (Γ)$ . We study complementary equienergetic c…

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.NT2019

A reduction formula for Waring numbers through generalized Paley graphs

Ricardo A. Podestá, Denis E. Videla

We give a reduction formula for the Waring number $g (k, q)$ over a finite field $F_{q}$ . By exploiting the relation between $g (k, q)$ with the diameter of the generalized Pale…

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…

math.NT2017

Block-transitive algebraic geometry codes attaining the Tsfasman-Vladut-Zink bound

María Chara, Ricardo A. Podestá, Ricardo Toledano

We study the asymptotic behavior of a family of algebraic geometry codes, which we call block-transitive, that generalizes the classes of transitive and quasi-transitive codes. We…

math.CO2016★ 1 cited

New identities for binary Krawtchouk polynomials, binomial coefficients and Catalan numbers

Ricardo A. Podestá

We obtain new combinatorial identities for integral values of binary Krawtchouk polynomials $K_{p}^{2 m} (x)$ , $0 \leq p \leq 2 m$ , by computing the characters of the $p$ -exterior represent…

math.NT2016

Asymptotically good 4-quasi transitive algebraic geometry codes over prime fields

María Chara, Ricardo Toledano, Ricardo Podestá

We study the asymptotic behavior of a family of algebraic geometry codes which are 4-quasi transitive linear codes. We prove that this family is asymptotically good over many prime…

math.DG2014

The eta function and eta invariant of $Z_{2^{r}}$ -manifolds

Ricardo A. Podestá

We compute the eta function $η (s)$ and its corresponding $η$ -invariant for the Atiyah-Patodi-Singer operator $D$ acting on an orientable compact flat manifold of dimensio…

The weight enumerators of irreducible cyclic codes of length 2ℓ

The spectral relation between irreducible cyclic codes and generalized Paley graphs

On regular graphs equienergetic with their complements

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

Isometries between finite groups

A reduction formula for Waring numbers through generalized Paley graphs

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

Block-transitive algebraic geometry codes attaining the Tsfasman-Vladut-Zink bound

New identities for binary Krawtchouk polynomials, binomial coefficients and Catalan numbers

Asymptotically good 4-quasi transitive algebraic geometry codes over prime fields

The eta function and eta invariant of Z2r​-manifolds

The weight enumerators of irreducible cyclic codes of length $2^{ℓ}$

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

The eta function and eta invariant of $Z_{2^{r}}$ -manifolds