11 problems

Let $m$ be even and consider the power function $F(x)=x^{4(2^m-1)+1}$ over $\mathbb{F}_{2^{2m}}$. Its cross-correlation should take at most five distinct values. Niho's conjecture.…

Cross-correlation bound conjecture. This bound also holds for $C(\mathcal{L}_q)$, up to a few exceptions among the small values $q\leq 59$. The bound is known computationally for a…

Cross-correlation bound conjecture. The bound of Theorem 2 holds for the maximal cross-correlation $C(\mathcal{L}_q)$, up to a few exceptions with $q\le 59$; explicitly, with $t$ t…

Let $r$ be a positive integer, let $n=3r$, and let $d=3^r+2$ or $d=3^{2r}+2$. Let $s$ be a ternary $m$-sequence of period $3^n-1$. Theorem 1 gives the cross-correlation values betw…

Gcd-dependence conjecture. For any positive integer $k$,

Helleseth's conjecture. If $m$ is a power of $2$, then $C_d(t)$ is not three-valued.

Let $m=2n$, and let $d$ be a decimation satisfying … with the congruence understood as $d(2^l+1)=2^i\pmod{2^n-1}$, and suppose that $\gcd(l,n)=1$. The cross-correlation function…

Let $m>10$, and consider decimations $d$ in the cross correlation between an $m$-sequence of period $2^m-1$ and the $d$-decimation of an $m$-sequence of period $2^n-1$, where…

Let $m=2n$ be even, and let $d$ be a decimation defining the cross correlation between an $m$-sequence of period $2^m-1$ and the $d$-decimation of an $m$-sequence of period $2^n-1$…

W1–G2 cross-correlation conjecture.

G2 cross-correlation conjecture.