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On duplication-free codes for disjoint or equal-length errors

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Abstract

Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-duplication errors, and equal-length tandem-duplication errors. We construct codes, with positive asymptotic rate, for the two settings, as well as for their combination. Our constructions are duplication-free codes, comprising codewords that do not contain tandem duplications of specific lengths. Additionally, our codes generalize previous constructions, containing them as special cases.

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No datasets were generated or analysed during the current study.

Notes

  1. The codes \(C_F\) in [11] contain all the duplication-free strings of length up to n, with a proper padding to make them all of length n.

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Acknowledgements

This work was supported in part by the Zhejiang Lab BioBit Program (grant no. 2022YFB507). The author M. Schwartz is currently on a leave of absence from Ben-Gurion University of the Negev.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, 8410501, Beer Sheva, Israel

    Wenjun Yu & Moshe Schwartz

  2. Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Moshe Schwartz

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  1. Wenjun Yu
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  2. Moshe Schwartz
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All authors contributed to the design and implementation and wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Wenjun Yu.

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Communicated by T. Feng.

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Yu, W., Schwartz, M. On duplication-free codes for disjoint or equal-length errors. Des. Codes Cryptogr. 92, 2845–2861 (2024). https://doi.org/10.1007/s10623-024-01417-7

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