Construction of Duplication Correcting Codes

Abstract

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. INDEX TERMSError correction codes, DNA computing, data storage systems, error analysis, duplication error. MORTEZA ESMAEILI received the M.S. degree in mathematics from the Teacher Training University of Tehran, Iran, in 1988, and the Ph.D. degree in mathematics (coding theory) from Car-

On Duplication-Free Codes for Disjoint or Equal-Length Errors

“…In the case of the code C F from Theorem 5, we do not know ℓ. We do, however, know the length of the transmitted string, n, and so, necessarily, ℓ ⩽ n and ℓ ∈ L. We can now try all possible ℓ ∈ L, ℓ ⩽ n, and see whether (6) results in a decoded string of length n. By Theorem 5, we are guaranteed only one choice of ℓ is possible. The decoding complexity is O(nN ) = O(N 2 ).…”

“…Interest in correcting duplication errors has expanded significantly. Codes correcting any number of tandem duplications were studied in [4][5][6], reverse duplications in [6], and reverse-complement duplications in [7]. Codes that correct only a fixed number of tandem duplications (sometimes just one) were studied in [8][9][10], reverse duplications in [11], and reverse-complement duplications in [12].…”