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Two-Insertion/Deletion/Substitution Correcting Codes
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abstract
In recent years, the emergence of DNA storage systems has led to a widespread focus on the research of codes correcting insertions, deletions, and classic substitutions. During the initial investigation, Levenshtein discovered the VT codes are precisely capable of correcting single insertion/deletion and then extended the VT construction to single-insertion/deletion/substitution ($1$-ins/del/sub) correcting codes. Inspired by this, we generalize the recent findings of $1$-del $1$-sub correcting codes with redundancy $6\log_{2}n+O(1)$ to more general $2$-ins/del/sub correcting codes without increasing the redundancy. Our key technique is to apply higher-order VT syndromes to distinct objects and accomplish a systematic classification of all error patterns.
Forward citations
Cited by 2 Pith papers
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On the Maximum Size of Codes Under the Damerau-Levenshtein Metric
For codes correcting constant numbers of deletions, insertions, substitutions, and adjacent transpositions, maximum size is at most C q^n / n^t, proving redundancy at least t log n minus O(1).
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Correcting Errors Through Partitioning and Burst-Deletion Correction
A partitioning theorem reduces t-deletion plus s-substitution correction to burst-deletion correction, yielding VT-based codes that match or slightly improve known redundancy bounds.
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