Correcting Errors Through Partitioning and Burst-Deletion Correction

In this paper, we propose a partitioning technique that decomposes a pair of sequences with overlappingt-deletions-substitution balls into sub-pairs, where the≤t-burst-deletion balls of each sub-pair intersect. This decomposition facilitates the development oft-deletions-substitution correcting codes that leverage approaches from≤t-burst-deletion correction. Building upon established approaches in the≤t-burst-deletion correction domain, we constructt-deletions-substitution correcting codes fort∈ {1, 2} over binary alphabets and fort= 1 in non-binary alphabets, with some constructions matching existing results and others outperforming current methods. Our framework offers new insights into the underlying principles of prior works, elucidates the limitations of current approaches, and provides a unified perspective on error correction strategies.