Arne Winterhof

activity

20082023

most citedExpansion complexity and linear complexity of sequences over finite fields

20 citations · 30 across the 30 of their papers we have counts for

collaborators

Showing 2020Show all

6 papers · 1 filter

math.NT2020★ 1 cited

Additive double character sums over some structured sets and applications

Cathy Swaenepoel, Arne Winterhof

We study additive double character sums over two subsets of a finite field. We show that if there is a suitable rational self-map of small degree of a set $D$ , then this set contai…

math.CO2020

On the Index of Diffie-Hellman Mapping

Leyla Işık, Arne Winterhof

Let $γ$ be a generator of a cyclic group $G$ of order $n$ . The least index of a self-mapping $f$ of $G$ is the index of the largest subgroup $U$ of $G$ such that $f (x) x^{- r}$ is co…

math.NT2020

A Note on the Cross-Correlation of Costas Permutations

Domingo Gomez-Perez, Arne Winterhof

We build on the work of Drakakis et al. (2011) on the maximal cross-correlation of the families of Welch and Golomb Costas permutations. In particular, we settle some of their conj…

math.NT2020

On the distribution of the Rudin-Shapiro function for finite fields

Cécile Dartyge, László Mérai, Arne Winterhof

Let $q = p^{r}$ be the power of a prime $p$ and $(β_{1}, \dots, β_{r})$ be an ordered basis of $F_{q}$ over $F_{p}$ . For $$ ξ=\sum\limits_{j=1}^r x_jβ_j\in \mathbb{F}_q \quad…

math.NT2020

Binary sequences derived from differences of consecutive quadratic residues

Arne Winterhof, Zibi Xiao

For a prime $p \geq 5$ let $q_{0}, q_{1}, \dots, q_{(p - 3) /2}$ be the quadratic residues modulo $p$ in increasing order. We study two $(p - 3) /2$ -periodic binary sequences $(d_{n})$ and $(t_{n})$ …

math.CO2020

The Spherical Kakeya Problem in Finite Fields

Mehdi Makhul, Audie Warren, Arne Winterhof

We study subsets of the $n$ -dimensional vector space over the finite field $F_{q}$ , for odd $q$ , which contain either a sphere for each radius or a sphere for each first coo…