5 problems

Let $q$ be the alphabet size, let $n$ be the length, and let $m$ be the number of component sequences. Write $E_n^{(m)}$ for the expected linear complexity of an $m$-multisequence…

Let $n\geq 3$, let $c$ be an integer satisfying … and suppose $c\neq 2^{n-1}+n+1$. A span $n$ de Bruijn sequence is a cyclic binary sequence in which every binary word of length…

Omega linear-complexity conjecture.

General asymptotic conjecture. As the size of $\text{\bf A}$ increases, ${\cal L}_n(\text{\bf A})$ approaches ${\cal L}_n(\text{\bf C})$ or ${\cal L}_n(\text{\bf F})$, according as…

Linear-complexity conjecture. If $2^{p-1}\not\equiv 1\pmod {p^2}$, then the linear complexity $L$ of $s^\infty$ is