3 problems

Let $A(n,1)$ denote the maximum size of a binary single-deletion-correcting code of length $n$, and let $VT_0(n)$ be the binary Varshamov–Tenengolts code with syndrome $0$. A code…

For a binary word length $n$, let a single-deletion-correcting code be a set of binary codewords whose deletion balls are pairwise disjoint, and let $\mathrm{VT}_0(n)$ denote the V…

Varshamov–Tenengolts optimality conjecture. In the binary case, the Varshamov–Tenengolts codes are the largest single-deletion correcting codes; in particular, ${\rm VT}_0(n)$ is o…