7 problems

Golomb's conjecture. If $w$ has the R-3 property, then $w$ can be generated by an LFSR.

Chang's conjecture. Any two binary de Bruijn sequences obtained from maximal-period linear feedback shift register sequences of the same order $k$ have the same number of cross-joi…

Least-period conjecture. The least periods of the family of generalized self-shrinking sequences belong to

Let $m$ and $n$ be positive integers. A primitive $c3$-LFSR of order $n$ over ${\mathbb F}_{q^m}$ is a word-oriented feedback shift register whose associated sequence has maximal p…

Let $q$ be a prime power, and let $m,n$ be positive integers. A primitive vector recurrence of order $n$ over ${\mathbb F}_q^m$ is a recurrence whose every nonzero initial state ge…

Fiber Conjecture. For every $f(X)\in {\EuScript P}(mn;q)$, the cardinality of $\Psi^{-1}(f(X))$ is independent of the choice of $f(X)$ and equals

Zeng–Han–He conjecture. The number of primitive $\sigma$-LFSRs of order $n$ over $\mathbb F_{q^m}$ is