4 problems

Let $\mathcal{M}$ be a binary $m$-sequence of period $2^n-1$, where $n\in\mathbb{N}$. For an integer shift $\tau$ with $1\leq\tau<2^n-1$, let $\mathcal{A}^{A}_{\mathcal{M}}(\tau)$…

Let $p$ be any odd prime, let $n$ be a positive integer, and set $N=p^n-1$. Let $\{s_t\}_{t=0}^{N-1}$ be the LSB sequence of a $p$-ary $m$-sequence of order $n$, and let $C_p$ deno…

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…