9 problems

Let $q=2^e$ with $e$ an even positive integer, let $u$ be a generator of $\mu_{q+1}$, and for $\alpha\in{\mathbb F}_{q}^*$ define $g_\alpha$ on ${\mathbb F}_{q^2}$ by…

Let $q=2^e$ with $e$ an even positive integer, let ${\bb F}_{q^2}$ be the finite field of order $q^2$, and for each $\alpha\in{\bb F}_{q}^*$ define … where $\sigma(X)=X+X^d+X^{dq}$…

Tokareva–Shapovalov conjecture. The function $f$ is a derivative of a bent function.

Exponential-growth conjecture. For any given $\ell$ in the range $1\leq \ell\leq m$, the number of inequivalent codes with these parameters obtained from $(2m,\ell)$ bent vectorial…

Conjectural Gauss-sum formula. There exists a Boolean function $h_{a,b}(\omega)$ such that

Bentness conjecture. The function $f_{a,b}$ is bent if and only if $K_{n/2}(a)=4$.

Let $f:GF(p)^n\to GF(p)$ be an even bent function with $p>2$ and $f(0)=0$. For each value of $f$, its level curve is the corresponding level set; assume these level curves give ris…

Let $p>2$ and let $f:GF(p)^n\to GF(p)$ be a weakly regular bent function corresponding to a weighted strongly regular graph via the stated analogy. Let $\mu_{ii}$ denote the diagon…

A Boolean function is homogeneous if all its monomials have the same degree, and rotation symmetric if it is invariant under cyclic permutations of its variables. A Boolean functio…