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Construction of single-deletion-correcting DNA codes using CIS codes

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Abstract

We find a method for constructing DNA codes with single-deletion-correcting capability. We first present an explicit algorithm for the construction of the q-ary single-deletion-correcting codes (abbreviated as SDC codes) using a class of the complementary information set codes (abbreviated as CIS codes), where q is a power of a prime. We then show that the encoding/decoding scheme of the CIS codes with single-deletion-correcting capability has a simple deterministic algorithm. Finally, applying our algorithm to the generated DNA codes with appropriate modification, we obtain the DNA codes with single-deletion-correcting capability. We present some various examples of such DNA codes, and we also obtain some lower bounds on the maximum size of the single-deletion-correcting DNA codes.

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Acknowledgements

We thank anonymous referees for their helpful comments, which improved the clarity of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Sogang University, Seoul, 04107, Republic of Korea

    Whan-Hyuk Choi

  2. University College, Yonsei University, 85 Songdogwahak-ro, Yeonsu-gu, Incheon, 21983, Republic of Korea

    Hyun Jin Kim

  3. Department of Mathematics, Ewha Womans University, 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul, 03760, Republic of Korea

    Yoonjin Lee

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  1. Whan-Hyuk Choi
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Correspondence to Hyun Jin Kim.

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Communicated by C. Carlet.

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W.-H. Choi: is supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (NRF-2019R1I1A1A01057755), H.J. Kim: is supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (NRF-2017R1D1A1B03028251) and (NRF-2020R1F1A1A01071645), and Y. Lee: is supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177) and also by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MEST)(NRF-2017R1A2B2004574).

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Choi, WH., Kim, H.J. & Lee, Y. Construction of single-deletion-correcting DNA codes using CIS codes. Des. Codes Cryptogr. 88, 2581–2596 (2020). https://doi.org/10.1007/s10623-020-00802-2

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  • DOI: https://doi.org/10.1007/s10623-020-00802-2

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