  Motivated by applications in DNA-based storage, we introduce the new problem
of code design in the Damerau metric. The Damerau metric is a generalization of
the Levenshtein distance which, in addition to deletions, insertions and
substitution errors also accounts for adjacent transposition edits. We first
provide constructions for codes that may correct either a single deletion or a
single adjacent transposition and then proceed to extend these results to codes
that can simultaneously correct a single deletion and multiple adjacent
transpositions. We conclude with constructions for joint block deletion and
adjacent block transposition error-correcting codes.
