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On conflict free DNA codes

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Abstract

DNA storage has emerged as an important area of research. The reliability of a DNA storage system depends on designing those DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy the newly introduced constraint, a generalization of the non-homopolymers constraint. In particular, each codeword of the DNA code has the specific property that any two consecutive sub-strings of the DNA codeword will not be the same. This is apart from the usual constraints such as Hamming, reverse, reverse-complement and GC-content. We believe that the new constraints proposed in this paper will provide significant achievements in reducing the errors, during reading and writing data into the synthetic DNA strings. We also present a construction (based on a variant of stochastic local search algorithm) to determine the size of the DNA codes with a constraint that each DNA codeword is free from secondary structures in addition to the usual constraint. This further improves the lower bounds from the existing literature, in some specific cases. A recursive isometric map between binary vectors and DNA strings is also proposed. By applying this map over the well known binary codes, we obtain classes of DNA codes with all of the above constraints, including the property that the constructed DNA codewords are free from the hairpin like secondary structures.

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Authors and Affiliations

  1. Laboratory of Natural Information Processing, Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat, India

    Krishna Gopal Benerjee, Sourav Deb & Manish K. Gupta

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  1. Krishna Gopal Benerjee
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  2. Sourav Deb
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  3. Manish K. Gupta
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Correspondence to Manish K. Gupta.

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The preliminary version of the paper is available at https://arxiv.org/abs/1902.04419

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Benerjee, K.G., Deb, S. & Gupta, M.K. On conflict free DNA codes. Cryptogr. Commun. 13, 143–171 (2021). https://doi.org/10.1007/s12095-020-00459-7

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