| Summary: | 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>.
|
|---|