  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 most $t$
deletions in non-binary sequences. We first propose a non-binary code
correcting a burst of at most 2 deletions for $q$-ary alphabets. Afterwards, we
extend this result to the case where the length of the burst can be at most $t$
where $t$ is 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.
