TY - JOUR
T1 - Designing DNA codes from reversible self-dual codes over GF(4)
AU - Kim, Hyun Jin
AU - Choi, Whan Hyuk
AU - Lee, Yoonjin
N1 - Funding Information:
Supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03028251) and (NRF-2020R1F1A1A01071645).Supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education(NRF-2019R1I1A1A01057755).Supported by the National Research Foundation of Korea (NRF) grant funded by (MEST) NRF-2017R1A2B2004574 and also by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177).
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/1
Y1 - 2021/1
N2 - We present an explicit method for designing DNA codes from reversible self-dual codes over the finite field GF(4) of order 4. We use Euclidean reversible self-dual codes (Euclidean RSD codes for short) since they have some advantages in designing DNA codes; hence, in this work RSD codes mean Euclidean RSD codes. We first work on a construction method for reversible self-dual codes over GF(4), and we study their properties in the aspect of their connection to DNA codes. We then obtain an efficient and feasible algorithm for designing DNA codes from RSD codes over GF(4). We point out that our algorithm takes advantage of reversibility and self-duality of RSD codes over GF(4). Finally, we produce DNA codes up to length 42 using our method and discuss the GC-weight distributions of DNA codes. We obtain many new DNA codes with better parameters when compared to the previously known results, and we also improve the lower bounds on the maximum size of DNA codes of a fixed code length and dimension.
AB - We present an explicit method for designing DNA codes from reversible self-dual codes over the finite field GF(4) of order 4. We use Euclidean reversible self-dual codes (Euclidean RSD codes for short) since they have some advantages in designing DNA codes; hence, in this work RSD codes mean Euclidean RSD codes. We first work on a construction method for reversible self-dual codes over GF(4), and we study their properties in the aspect of their connection to DNA codes. We then obtain an efficient and feasible algorithm for designing DNA codes from RSD codes over GF(4). We point out that our algorithm takes advantage of reversibility and self-duality of RSD codes over GF(4). Finally, we produce DNA codes up to length 42 using our method and discuss the GC-weight distributions of DNA codes. We obtain many new DNA codes with better parameters when compared to the previously known results, and we also improve the lower bounds on the maximum size of DNA codes of a fixed code length and dimension.
KW - Code over finite field of order 4
KW - Construction of DNA code
KW - Fixed GC-contents
KW - Reverse-complement constraint
KW - Reversible self-dual code
UR - http://www.scopus.com/inward/record.url?scp=85091755922&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2020.112159
DO - 10.1016/j.disc.2020.112159
M3 - Article
AN - SCOPUS:85091755922
SN - 0012-365X
VL - 344
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1
M1 - 112159
ER -