Synchronization and substitution error-correcting codes for the Levenshtein metric

Abstract

Block codes are constructed that are capable of simultaneously correctingeor fewer synchronization errors intconsecutive words, for anyt geq 2e + 1, andsor fewer substitution errors in eachoft - 1or fewer of these words under the condition that there exists at least one ungarbled word among thetconsecutive words. Also, some new extensions of theA_{n}^{c}codes of Calabi and Hartnett are presented under the condition that synchronization and substitution errors do not coexist in thetconsecutive words.