2 problems

Let $q$ be an odd prime power, let $\theta$ be primitive in $\mathbb{F}_q$, and let $Z_{n,\theta}$ be the Sidelnikov sequence of length $n=q-1$ with respect to $\theta$. Let $F$ de…

Let $F=\mathbb{F}_{2^d}$ and let $K$ be a subfield of size $2^k$, where $k$ divides $d$. Let $\theta$ be primitive in $F$, let $\ell$ be coprime to $2^k-1$, and let the Gordon-Mill…