Non-Binary Codes for Correcting a Burst of at Most t Deletions

This is the authors' abstract. We don't add key points for this paper.

The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at mosttdeletions in non-binary sequences. When the alphabet sizeqis even, we first propose a non-binary code correcting a burst of at most 2 deletions forq-ary alphabets. Afterwards, we extend this result to the case where the length of the burst can be at mosttwheretis a constant. Finally, we consider the setup where the sequences that are transmitted are permutations. The proposed codes are the largest known for their respective parameter regimes.