4 problems

Chen et al.'s arithmetic autocorrelation distribution conjecture. The arithmetic autocorrelation satisfies

Let $r$ be a positive integer with $(r,3)=3$, and consider the cross correlation of a ternary $m$-sequence of period $3^{3r}-1$ with its decimation $d=3^r+2$ or $d=3^{2r}+2$. The c…

Let $p$ be a prime, let $n$ be a positive integer, and let $d$ be a decimation parameter. Define $\text{S}_d(z)=\text{C}_d(z)+1$, where $z\in\operatorname{GF}(p^n)^*$. Helleseth's…

Let $n=2t$ and $p=2$. Define the cross-correlation quantity $\text{S}_d(z)=\text{C}_d(z)+1$. Sarwate et al.'s conjecture. One has … The paper states that this conjecture is confirm…