Reversible and Reversible-Complement Double Cyclic Codes over F4+vF4 and its Application to DNA Codes
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| Format: | Preprint |
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2025
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| _version_ | 1866908712560492544 |
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| author | Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G. |
| author_facet | Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G. |
| contents | In this article, we study the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4$ and we give a necessary and sufficient condition for a double cyclic code over $\mathbb{F}_4$ to be reversible. Also, we determine the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4+v\mathbb{F}_4$ with $v^2=v$, satisfying the reverse constraint and the reverse-complement constraint. Then we establish a one-to-one correspondence $ψ$ between the 16 DNA double pairs $S_{D_{16}} $ and the 16 elements of the finite ring $\mathbb{F}_4+v\mathbb{F}_4$. We also discuss the GC-content of DNA double cyclic codes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reversible and Reversible-Complement Double Cyclic Codes over F4+vF4 and its Application to DNA Codes Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G. Rings and Algebras Information Theory In this article, we study the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4$ and we give a necessary and sufficient condition for a double cyclic code over $\mathbb{F}_4$ to be reversible. Also, we determine the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4+v\mathbb{F}_4$ with $v^2=v$, satisfying the reverse constraint and the reverse-complement constraint. Then we establish a one-to-one correspondence $ψ$ between the 16 DNA double pairs $S_{D_{16}} $ and the 16 elements of the finite ring $\mathbb{F}_4+v\mathbb{F}_4$. We also discuss the GC-content of DNA double cyclic codes. |
| title | Reversible and Reversible-Complement Double Cyclic Codes over F4+vF4 and its Application to DNA Codes |
| topic | Rings and Algebras Information Theory |
| url | https://arxiv.org/abs/2512.13295 |