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The problem of correcting deletions and insertions has recently receivedsignificantly increased attention due to the DNA-based data storage technology,which suffers from deletions and insertions with extremely high probability. Inthis work, we study the problem of constructing non-binaryburst-deletion/insertion correcting codes. Particularly, for the quaternaryalphabet, our designed codes are suited for correcting a burst ofdeletions/insertions in DNA storage.  Non-binary codes correcting a single deletion or insertion were introduced byTenengolts [1984], and the results were extended to correct a fixed-lengthburst of deletions or insertions by Schoeny et al. [2017]. Recently, Wang etal. [2021] proposed constructions of non-binary codes of length n, correcting aburst of length at most two for q-ary alphabets with redundancy log n+O(log qlog log n) bits, for arbitrary even q. The common idea in those constructionsis to convert non-binary sequences into binary sequences, and the errordecoding algorithms for the q-ary sequences are mainly based on the success ofrecovering the corresponding binary sequences, respectively. In this work, welook at a natural solution in which the error detection and correctionalgorithms are performed directly over q-ary sequences, and for certain cases,our codes provide a more efficient encoder with lower redundancy than thebest-known encoder in the literature.

A New Version of q-ary Varshamov-Tenengolts Codes with More Efficient Encoders: The Differential VT Codes and The Differential Shifted VT Codes