Motivated by their applications in DNA-based storage systems, codes capable of correcting consecutive deletions have attracted significant attention. An important class of such codes consists of those that can correct multiple consecutive deletion errors, commonly referred to as multiple $b$-burst deletion-correcting codes. In this paper, we investigate the fundamental limits of multiple $b$-burst deletion-correcting codes. Specifically, we first characterize several structural properties of the associated deletion balls. Then, leveraging these properties, we derive several upper bounds and a combinatorial lower bound on the maximum size of such codes. As a consequence, our bounds improve upon the previously known results for general parameter regimes and are shown to be asymptotically optimal for certain cases.

翻译：受其在基于DNA存储系统中应用的启发，能够纠正连续删除错误的码受到了广泛关注。这类码中一个重要类别是可以纠正多个连续删除错误的码，通常称为多个$b$-突发删除纠正码。本文研究了多个$b$-突发删除纠正码的基本极限。具体而言，我们首先刻画了相关删除球的若干结构性质。进而利用这些性质，推导了这类码最大规模的若干上界和一个组合下界。作为结果，我们的界在一般参数范围内改进了先前已知结果，并在某些情况下证明了其渐近最优性。