1 citations · 3 across the 6 of their papers we have counts for
15 papers
Character sums over sparse elements of finite fields
László Mérai, Igor E. Shparlinski, Arne Winterhof
We estimate mixed character sums of polynomial values over elements of a finite field with sparse representations in a fixed ordered basis over the subfield $\mat…
On divisors of sums of polynomials
László Mérai
Let and be sets of polynomials of degree over a finite field. We show, that if and are large enough, then has an i…
Pseudorandom sequences derived from automatic sequences
László Mérai, Arne Winterhof
Many automatic sequences, such as the Thue-Morse sequence or the Rudin-Shapiro sequence, have some desirable features of pseudorandomness such as a large linear complexity and a sm…
Linear complexity of some sequences derived from hyperelliptic curves of genus 2
Vishnupriya Anupindi, László Mérai
For a given hyperelliptic curve over a finite field with Jacobian , we consider the hyperelliptic analogue of the congruential generator defined by for $n\…
On functions with the maximal number of bent components
Nurdagül Anbar, Tekgül Kalaycı, Wilfried Meidl +1
A function , , can have at most bent component functions. Trivial examples are obtained as $F(x) = (f_1(x),\ldots,f_m(x)…
On the Dynamical System Generated by the Möbius transformation at Prime Times
László Mérai, Igor E. Shparlinski
We study the distribution of the sequence of elements of the discrete dynamical system generated by iterations of the Möbius map over a finite field of…
Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes
Fabrizio Barroero, Laura Capuano, László Mérai +2
For positive integers and , we introduce and study the notion of -multiplicative dependence over the algebraic closure of a finite prime field $…
On the distribution of the Rudin-Shapiro function for finite fields
Cécile Dartyge, László Mérai, Arne Winterhof
Let be the power of a prime and be an ordered basis of over . For $$ ξ=\sum\limits_{j=1}^r x_jβ_j\in \mathbb{F}_q \quad…
On digits of Mersenne numbers
Bryce Kerr, László Mérai, Igor E. Shparlinski
Motivated by recently developed interest to the distribution of -ary digits of Mersenne numbers , where is prime, we estimate rational exponential sums with $M_…
Values of rational functions in small subgroups of finite fields and the identity testing problem from powers
László Mérai
Motivated by some algorithmic problems, we give lower bounds on the size of the multiplicative groups containing rational function images of low-dimensional affine subspaces of a f…
Algebraic dependence in generating functions and expansion complexity
Domingo Gómez-Pérez, László Mérai
In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. Recently, a series of paper has been published for analysis of expansion com…
Dynamical irreducibility of polynomials modulo primes
László Mérai, Alina Ostafe, Igor E. Shparlinski
For a class of polynomials , which in particular includes all quadratic polynomials, and also trinomials of some special form, we show that, under some natural…
Unlikely intersections over finite fields: polynomial orbits in small subgroups
László Mérai, Igor E. Shparlinski
We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of elements. We also give a lower bound on the size of the s…
Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields
László Mérai, Igor E. Shparlinski
For a prime and a polynomial over a finite field of elements, we give upper bounds on the number of solutions $$ F(x,y)=0, \quad x\in\mathcal{A}, \…
On the th linear complexity of automatic sequences
László Mérai, Arne Winterhof
The th linear complexity of a sequence is a measure of predictability. Any unpredictable sequence must have large th linear complexity. However, in this paper we show that fo…