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arXiv · 2507.13808

Asymptotically Optimal Codes Correcting One Substring Edit

Yuting Li·Yuanyuan Tang·Hao Lou·Ryan Gabrys·Farzad Farnoud
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Abstract

The substring edit error is the operation of replacing a substring $u$ of $x$ with another string $v$, where the lengths of $u$ and $v$ are bounded by a given constant $k$. It encompasses localized insertions, deletions, and substitutions within a window. Codes correcting one substring edit have redundancy at least $\log n+k$. In this paper, we construct codes correcting one substring edit with redundancy $\log n+O(\log \log n)$, which is asymptotically optimal.

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Yuting Li, Yuanyuan Tang, Hao Lou, Ryan Gabrys, Farzad Farnoud. 2025-07-18. Asymptotically Optimal Codes Correcting One Substring Edit. https://arxiv.org/abs/2507.13808

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