Construction of Duplication Correcting Codes

Palindromic duplication (PD) and tandem duplication (TD) errors can occur when the DNA of a living organism is used to store data. In this work, we construct codes which can correct any number of PD errors of fixed length k where k = 2, 3. Codes are also constructed to correct a combination of TD errors of fixed length k and PD errors of fixed length k where k = 2, 3. We introduce k-clamp free irreducible words and use them to construct codes which can correct any combination of k-TD and k-PD errors where k = 2, 3. The extension of these constructions to k > 3 is conjectured.