11 citations · 15 across the 18 of their papers we have counts for
20 papers
A Kronecker algorithm for locally closed sets over a perfect field
Nardo Giménez, Joos Heintz, Guillermo Matera +3
We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety defined over a perf…
Estimates on the number of rational solutions of Markoff-Hurwitz equations over finite fields
Miriam Abdon, Daniela Alves de Oliveira, Juliane Capaverde +2
Let denote the number of solutions to the generalized Markoff-Hurwitz-type equation \[(a_1X_1^m+\cdots + a_nX_n^m+a)^k=bX_1\cdots X_n \] over the finite field , w…
Singularly cospectral circulant graphs
Cristian M. Conde, Ezequiel Dratman, Luciano N. Grippo +1
Two graphs having the same spectrum are said to be cospectral. Two graphs such that the absolute values of their nonzero eigenvalues coincide are singularly cospectral graphs. Cosp…
An approach to the moments subset sum problem through systems of diagonal equations over finite fields
Juan Francisco Gottig, Mariana Pérez, Melina Privitelli
Let be the finite field of elements, for a given subset , , an integer and …
Smooth symmetric systems over a finite field and applications
Nardo Giménez, Guillermo Matera, Mariana Pérez +1
We study the set of common -rational solutions of "smooth" systems of multivariate symmetric polynomials with coefficients in a finite field . We show t…
The distribution of defective multivariate polynomial systems over a finite field
Nardo Giménez, Guillermo Matera, Mariana Pérez +1
This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ide…
On the computation of rational solutions of underdetermined systems over a finite field
Nardo Giménez, Guillermo Matera, Mariana Pérez +1
We design and analyze an algorithm for computing solutions with coefficients in a finite field of underdetermined systems defined over . The algorithm…
Playing through a noisy channel (and knowing it)
Nicolas Capitelli, Melina Privitelli
In this note we discuss a theory of combinatorial games that involve transmitting the moves through a noisy channel that can introduce errors during the transmission. Players are a…
On the number of simultaneous solutions of certain diagonal equations over finite fields
Mariana Pérez, Melina Privitelli
In this paper we obtain explicit estimates and existence results on the number of -rational solutions of certain systems defined by families of diagonal equations ove…
Average-case complexity of the Euclidean algorithm with a fixed polynomial over a finite field
Nardo Giménez, Guillermo Matera, Mariana Pérez +1
We analyze the behavior of the Euclidean algorithm applied to pairs (g,f) of univariate nonconstant polynomials over a finite field F_q of q elements when the highest-degree polyno…
Estimates on the number of rational solutions of variants of diagonal equations over finite fields
Mariana Perez, Melina Privitelli
In this paper we study the set of rational solutions of equations defined by power sums symmetric polynomials with coefficients in a finite field. We do this by means of applying a…
Factorization patterns on nonlinear families of univariate polynomials over a finite field
Guillermo Matera, Mariana Pérez, Melina Privitelli
We estimate the number of elements on a nonlinear family of monic polynomials of of degree having factorization p…
On the value set of small families of polynomials over a finite field, III
Guillermo Matera, Mariana Pérez, Melina Privitelli
We estimate the average cardinality of the value set of a general family of monic univariate polynomials of degree with coefficients in…
Number of rational points of symmetric complete intersections over a finite field and applications
Guillermo Matera, Mariana Perez, Melina Privitelli
We study the set of common F_q-rational zeros of systems of multivariate symmetric polynomials with coefficients in a finite field F_q. We establish certain properties on these pol…
On the computation of rational points of a hypersurface over a finite field
Guillermo Matera, Mariana Pérez, Melina Privitelli
We design and analyze an algorithm for computing rational points of hypersurfaces defined over a finite field based on searches on "vertical strips", namely searches on parallel li…
Explicit Estimates for the Number of Rational Points of Singular Complete Intersections over a Finite Field
Guillermo Matera, Mariana Pérez, Melina Privitelli
Let be a complete intersection defined over a finite field of dimension and singular locus of dimensi…
On the value set of small families of polynomials over a finite field, II
Guillermo Matera, Mariana Pérez, Melina Privitelli
We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients a_{d-1},...,a_{d-s} a…
On the value set of small families of polynomials over a finite field, I
Eda Cesaratto, Guillermo Matera, Mariana Pérez +1
We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients a_{d-1},..., a_{d-s}…
Polar varieties, Bertini's theorems and number of points of singular complete intersections over a finite field
Antonio Cafure, Guillermo Matera, Melina Privitelli
Let P^n denote the n-dimensional projective space defined over the algebraic closure of a finite field F_q, let V contained P^n be a complete intersection defined over F_q of dimen…
Singularities of symmetric hypersurfaces and an application to Reed-Solomon codes
Antonio Cafure, Guillermo Matera, Melina Privitelli
We determine conditions on q for the nonexistence of deep holes of the standard Reed-Solomon code of dimension k over F_q generated by polynomials of degree k+d. Our conditions rel…