In this paper, for any fixed positive integers $t$ and $q>2$, 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：本文针对任意固定正整数 $t$ 和 $q>2$，构造了能够纠正最多 $t$ 次突发删除的 $q$ 元码，其冗余度为 $\log n+8\log\log n+o(\log\log n)+\gamma_{q,t}$ 比特，且具有近线性的编码/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。以往工作中，此类码的构造冗余度分别为 $\log n+O(\log q\log\log n)$ 比特或 $\log n+O(t^2\log\log n)+O(t\log q)$。新构造的冗余度在第二项中与 $q$ 和 $t$ 无关。