In this paper, we present an efficiently encodable and decodable code construction that is capable of correction a burst of deletions of length at most $k$. The redundancy of this code is $\log n + k(k+1)/2\log \log n+c_k$ for some constant $c_k$ that only depends on $k$ and thus is scaling-optimal. The code can be split into two main components. First, we impose a constraint that allows to locate the burst of deletions up to an interval of size roughly $\log n$. Then, with the knowledge of the approximate location of the burst, we use several {shifted Varshamov-Tenengolts} codes to correct the burst of deletions, which only requires a small amount of redundancy since the location is already known up to an interval of small size. Finally, we show how to efficiently encode and decode the code.

中文翻译：

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修正一连串变长删除的最优编码

在本文中，我们提出了一种有效的可编码和可解码的代码结构，它能够纠正长度最多为 $k$ 的突发删除。这段代码的冗余是 $\log n + k(k+1)/2\log \log n+c_k$ 对于一些仅依赖于 $k$ 的常量 $c_k$ 并且因此是缩放最优的。代码可以分为两个主要部分。首先，我们施加了一个约束，允许将删除的突发定位到大小约为 $\log n$ 的间隔内。然后，在知道突发的大致位置的情况下，我们使用几个{shifted Varshamov-Tenengolts}代码来纠正删除的突发，这仅需要少量的冗余，因为位置已经知道了一个小区间尺寸。最后，我们展示了如何有效地编码和解码代码。