In this paper, we provide criteria for the reversibility and conjugate-reversibility of 1-generator quasi-cyclic codes. The Chinese remainder theorem is used to provide a characterization for generalized quasi-cyclic codes to be Galois linear complementary-dual and Galois self-dual. Using the approach proposed by Güneri and Özbudak (IEEE Trans Inf Theory 59(2):979-985, 2013), a new concatenated structure for quasi-cyclic codes is given. We show that Galois linear complementary-dual quasi-cyclic codes are asymptotically good over some finite fields. In addition, DNA codes are given which have more codewords than previously known 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.
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-
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