Two-Insertion/Deletion/Substitution Correcting Codes

In recent years, the emergence of DNA storage systems has led to a widespread interest in codes correcting insertions, deletions, and classic substitutions. Levenshtein discovered that the VT codes are capable of correcting single insertion/deletion and then extended the VT construction to single-insertion/deletion/substitution correcting codes. Inspired by this, we employ the higher-order VT syndromes, which were initially introduced for 2-insertion/deletion correction, to construct 2-insertion/deletion/substitution correcting codes with redundancy $6\log _{2}n+8$ . Our key technical contributions include the formalization of sign-preserving number as a core concept in applying higher-order VT syndromes and the development of its analytical framework.