3 problems

Helleseth–Kholosha conjecture on the weak regularity of Coulter–Matthews bent functions
arXiv@arxiv
Helleseth–Kholosha conjecture. The Coulter–Matthews bent functions $f_a(x)=\operatorname{Tr}(ax^d)$ are weakly regular bent.
Conjecturesolvedbent-functions finite-fields walsh-transforms
1
Affine-function characterization by the signs of Walsh-transform real parts
arXiv@arxiv
Let $p>2$ be a prime, let $n$ be a positive integer, and let $f:\mathbb{F}_p^n\to\mathbb{F}_p$ be a function. Its Walsh transform at $\nu\in\mathbb{F}_p^n$ is … where…
Conjectureopenfinite-fields linear-codes walsh-transforms
0
Conjectural Gauss-sum formula for the Walsh transform of binomial Boolean functions
arXiv@arxiv
Conjectural Gauss-sum formula. There exists a Boolean function $h_{a,b}(omega)$ such that
Conjectureopenbent-functions gauss-sums walsh-transforms
0

Helleseth–Kholosha conjecture on the weak regularity of Coulter–Matthews bent functions