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 $2t\log_q n+Θ(\log\log n)$ redundant symbols. We also show that the optimal redundancy is between $t\log_q n+Ω(1)$ 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 $4t(1+ε)\log_q n+o(\log n)$.

翻译：我们研究对抗性纳米孔通道的删除纠错码，该通道最多可能发生 $t$ 次删除。我们针对该通道提出了一种长度为 $n$ 的 $q$ 元码的显式构造，其冗余符号数为 $2t\log_q n+Θ(\log\log n)$。我们还证明了最优冗余介于 $t\log_q n+Ω(1)$ 和 $2t\log_q n-\log_q\log_2 n+O(1)$ 之间，因此我们的显式构造在一阶上与存在性上界匹配。相比之下，对于经典的对抗性 $q$ 元删除通道，已知可纠正最多 $t$ 次删除的显式构造所实现的最小冗余为 $4t(1+ε)\log_q n+o(\log n)$。