Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> + <italic>v</italic>Z<sub>4</sub>
In this work, we investigate DNA codes of odd length over the finite ring <inline-formula> <tex-math notation="LaTeX">$R=\mathbb {Z}_{4}+v \mathbb {Z}_{4},v^{2}=v$ </tex-math></inline-formula>. Firstly, we give a map <inline-formula> <tex-math notation=&quo...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2020-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9113264/ |
| _version_ | 1811212317549920256 |
|---|---|
| author | Jie Liu Hualu Liu |
| author_facet | Jie Liu Hualu Liu |
| author_sort | Jie Liu |
| collection | DOAJ |
| description | In this work, we investigate DNA codes of odd length over the finite ring <inline-formula> <tex-math notation="LaTeX">$R=\mathbb {Z}_{4}+v \mathbb {Z}_{4},v^{2}=v$ </tex-math></inline-formula>. Firstly, we give a map <inline-formula> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">$R^{n}$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$\{A, T, G,C\}^{2n}$ </tex-math></inline-formula>. Then cyclic codes of odd length satisfying the reverse and reverse-complement constraint are characterized over such ring. Moreover, when <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> is a reverse-complement cyclic code over <inline-formula> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula>, we prove that <inline-formula> <tex-math notation="LaTeX">$\Phi (C)$ </tex-math></inline-formula> is a cyclic DNA code by using the method different from all the previously known ones, which helps us finding a new DNA code with 256 codewords. Finally, we consider the <inline-formula> <tex-math notation="LaTeX">$GC$ </tex-math></inline-formula> content of code <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> over finite ring <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}_{4} + v \mathbb {Z}_{4}$ </tex-math></inline-formula> by means of the Gray images of the minimal generating set of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula>. |
| first_indexed | 2024-04-12T05:27:20Z |
| format | Article |
| id | doaj.art-b966bc6fe51f4ef0b010841cef8fb94a |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-12T05:27:20Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-b966bc6fe51f4ef0b010841cef8fb94a2022-12-22T03:46:15ZengIEEEIEEE Access2169-35362020-01-01811120011120710.1109/ACCESS.2020.30012839113264Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> + <italic>v</italic>Z<sub>4</sub>Jie Liu0https://orcid.org/0000-0002-4193-7962Hualu Liu1School of Medicine, Hubei Polytechnic University, Huangshi, ChinaSchool of Science, Hubei University of Technology, Wuhan, ChinaIn this work, we investigate DNA codes of odd length over the finite ring <inline-formula> <tex-math notation="LaTeX">$R=\mathbb {Z}_{4}+v \mathbb {Z}_{4},v^{2}=v$ </tex-math></inline-formula>. Firstly, we give a map <inline-formula> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">$R^{n}$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$\{A, T, G,C\}^{2n}$ </tex-math></inline-formula>. Then cyclic codes of odd length satisfying the reverse and reverse-complement constraint are characterized over such ring. Moreover, when <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> is a reverse-complement cyclic code over <inline-formula> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula>, we prove that <inline-formula> <tex-math notation="LaTeX">$\Phi (C)$ </tex-math></inline-formula> is a cyclic DNA code by using the method different from all the previously known ones, which helps us finding a new DNA code with 256 codewords. Finally, we consider the <inline-formula> <tex-math notation="LaTeX">$GC$ </tex-math></inline-formula> content of code <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> over finite ring <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}_{4} + v \mathbb {Z}_{4}$ </tex-math></inline-formula> by means of the Gray images of the minimal generating set of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula>.https://ieeexplore.ieee.org/document/9113264/Reverse-complement cyclic codecyclic DNA codeWatson-Crick complement |
| spellingShingle | Jie Liu Hualu Liu Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> + <italic>v</italic>Z<sub>4</sub> IEEE Access Reverse-complement cyclic code cyclic DNA code Watson-Crick complement |
| title | Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> + <italic>v</italic>Z<sub>4</sub> |
| title_full | Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> + <italic>v</italic>Z<sub>4</sub> |
| title_fullStr | Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> + <italic>v</italic>Z<sub>4</sub> |
| title_full_unstemmed | Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> + <italic>v</italic>Z<sub>4</sub> |
| title_short | Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> + <italic>v</italic>Z<sub>4</sub> |
| title_sort | construction of cyclic dna codes over the ring z sub 4 sub x002b italic v italic z sub 4 sub |
| topic | Reverse-complement cyclic code cyclic DNA code Watson-Crick complement |
| url | https://ieeexplore.ieee.org/document/9113264/ |
| work_keys_str_mv | AT jieliu constructionofcyclicdnacodesovertheringzsub4subx002bitalicvitaliczsub4sub AT hualuliu constructionofcyclicdnacodesovertheringzsub4subx002bitalicvitaliczsub4sub |