Deletion-correcting codes for an adversarial nanopore channel

We study deletion-correcting codes for an adversarial nanopore channel in which at most $t$ deletions may occur. We propose an explicit construction of $q$-ary codes of length $n$ for this channel with $2t{\log }_{q}n+\mathrm{\Theta }(\log \log n)$ redundant symbols. We also show that the optimal redundancy is between $t{\log }_{q}n+\mathrm{\Omega }(1)$ and $2t{\log }_{q}n-{\log }_q{\log }_{2}n+O(1)$, so our explicit construction matches the existential upper bound to first order. In contrast, for the classical adversarial $q$-ary deletion channel, the smallest redundancy achieved by known explicit constructions that correct up to $t$ deletions is $4t(1+\epsilon ){\log }_{q}n+o(\log n)$.