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.
Bibliographical noteFunding Information:
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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- CIS code
- DNA code
- Synchronization-correcting code