Construction of tandem duplication correcting codes

Tandem duplication (TD) errors occur when data is stored in the DNA of living organisms. The construction of codes to correct these errors was previously considered. A method was proposed to construct codes for TD errors of length at most k , k = 2 , 3 , based on the uniqueness of ⩽ k ‐roots. It was shown that there exist words which have more than one ⩽ k ‐root when k > 3 . As a consequence, the previous approach to correcting TD errors of length at most k cannot be extended to k > 3 . In this study, ⩽ k ‐hinge‐free irreducible words are introduced and used to construct codes for TD errors of length at most k where 4 ⩽ k ⩽ 9 . Furthermore, it is conjectured that the proposed approach can be extended to k > 9 .