6 problems

Ahlswede's conjecture. The condition $S(\mathbf{v}_n)\leq\frac{3}{4}$ is sufficient for the existence of a binary fix-free code $C(\mathbf{v}_n)$.

Optimal symmetric fix-free code transformation conjecture. Suppose that $S_n,S_n^{'},C_n\in\mathbb{S}_n$, that $S_n$ lies in a shortest transformation from $R_n$ to $S_n^{'}$, and…

Let $q\geq2$, let $\mathcal A=\{0,\ldots,q-1\}$, and let $(\alpha_l)_{l\in\mathbb N}$ be a sequence of nonnegative integers with $\alpha_1=0$, $\alpha_2\leq1$, and … For a linear o…

Let a $P_\gamma$-simple extension class be the class notion defined in the survey for which the extension property holds with parameter $\gamma$. Simple-extension conjecture. … The…

Let $P_\gamma$ denote the property that every relevant partial fix-free code whose Kraftsum is at most $\gamma$ can be extended in the manner defined in the survey; let $\gamma^*$…

Let $q\binom{}{\geq}2$ and let $(\alpha_l)_{l\in\mathbb{N}}$ be a sequence of nonnegative integers. A fix-free code $\mathcal C\subseteq\mathcal A^*$ fits the sequence when…