Synchronization and substitution error-correcting codes for the Levenshtein metric

Block codes are constructed that are capable of simultaneously correcting
e
or fewer synchronization errors in
t
consecutive words, for any
t \geq 2e + 1
, and
s
or fewer substitution errors in eachof
t - 1
or fewer of these words under the condition that there exists at least one ungarbled word among the
t
consecutive words. Also, some new extensions of the
A_{n}^{c}
codes of Calabi and Hartnett are presented under the condition that synchronization and substitution errors do not coexist in the
t
consecutive words.