In this paper, for any fixed integer $q>2$, we construct $q$-ary codes correcting a burst of at most $t$ deletions with redundancy $\log n+8\log\log n+o(\log\log n)+\gamma_{q,t}$ bits and near-linear encoding/decoding complexity, where $n$ is the message length and $\gamma_{q,t}$ is a constant that only depends on $q$ and $t$. In previous works there are constructions of such codes with redundancy $\log n+O(\log q\log\log n)$ bits or $\log n+O(t^2\log\log n)+O(t\log q)$. The redundancy of our new construction is independent of $q$ and $t$ in the second term.

翻译：本文针对任意固定整数$q>2$，构造了纠正突发至多$t$个删除的$q$元码，其冗余度为$\log n+8\log\log n+o(\log\log n)+\gamma_{q,t}$比特，并具有近线性编码/解码复杂度，其中$n$为消息长度，$\gamma_{q,t}$为仅依赖于$q$和$t$的常数。此前的工作中，此类码的冗余度构造为$\log n+O(\log q\log\log n)$比特或$\log n+O(t^2\log\log n)+O(t\log q)$。本文新构造的冗余度在第二项中与$q$和$t$无关。