7 problems

Feasibility conjecture. Every integer

Let $C$ be a linear binary indel code of dimension $3$. Cheng et al.'s conjecture. There exists an absolute constant $\delta_0>0$ such that $C$ cannot correct a $1/2-\delta_0$ frac…

Let $\Sigma_q$ be an alphabet of size $q$, let $\mathcal{D}_t$ denote the deletion channel allowing $t$ deletions, and let $\rho(n,q,M;\mathcal{B})$ be the minimum size of an…

Let $H(n,q,s,a)$ denote a Helberg code with length $n$, alphabet size $q$, deletion parameter $s$, and residue $a$. Let $a$ be the residue corresponding to the maximum number of co…

Let $VT_{(a,b)}(n;4)$ be a quaternary Varshamov–Tenengolts code, let $\phi$ be a Naisargik map, and let $D_1(X)$ denote the set of binary sequences obtained from $X$ by one deletio…

VT-code upper-bound conjecture. The maximum size of an SDECC of length $11$ is

Let $k$ be the message length, let $cell$ and $c$ be Guess & Check (GC) code parameters with $cell=Omega(\log k)$ and $c\geq 2\delta$, and let $L_{max}$ denote the maximum list siz…