In the present paper, we study the structure of cyclic DNA codes of even length over the ring \({F}_2+u{F}_2+u^2{F}_2\) where \(u^3=0\). We investigate two presentations of cyclic codes of even length over \({F}_2+u{F}_2+u^2{F}_2\) satisfying the reverse constraint and the reverse-complement constraint.

中文翻译：

---

关于超过$$ {F} _2 + u {F} _2 + u ^ 2 {F} _2 $$ F 2 + u F 2 + u 2 F 2的循环DNA代码

在本文中，我们研究了在环\（{F} _2 + u {F} _2 + u ^ 2 {F} _2 \）上\（u ^ 3 = 0 \ ）。我们研究了满足反约束和反补约束的\（{F} _2 + u {F} _2 + u ^ 2 {F} _2 \）上偶数长度的循环码的两种表示形式。