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 $({\beta }_1,\dots ,{\beta }_r)$ be an ordered basis of ${\mathbb{F}}_q$ over ${\mathbb{F}}_p$. For $$ ξ=\sum\limits_{j=1}^r x_jβ_j\in \mathbb{F}_q \quad…