Designing DNA codes from reversible self-dual codes over GF(4)

Hyun Jin Kim; Whan Hyuk Choi; Yoonjin Lee

doi:10.1016/j.disc.2020.112159

Designing DNA codes from reversible self-dual codes over GF(4)

Hyun Jin Kim, Whan Hyuk Choi, Yoonjin Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

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.

Original language	English
Article number	112159
Journal	Discrete Mathematics
Volume	344
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2020.112159
State	Published - Jan 2021

Bibliographical note

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.

Keywords

Code over finite field of order 4
Construction of DNA code
Fixed GC-contents
Reverse-complement constraint
Reversible self-dual code

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title = "Designing DNA codes from reversible self-dual codes over GF(4)",

abstract = "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.",

keywords = "Code over finite field of order 4, Construction of DNA code, Fixed GC-contents, Reverse-complement constraint, Reversible self-dual code",

author = "Kim, {Hyun Jin} and Choi, {Whan Hyuk} and Yoonjin Lee",

note = "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: {\textcopyright} 2020 Elsevier B.V.",

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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.

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Designing DNA codes from reversible self-dual codes over GF(4)

Abstract

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Keywords

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