We study the algebraic structure of DNA codes constructed over the ring R=F₂ u, v, w ⟨u²=v², uv=0, w²=w⟩, which is a commutative local Frobenius non-chain ring. We define a gray map over R and generate DNA codes using the images of the gray map. We define reversible DNA codes and reversible complement DNA codes over the ring.
Merve Bulut Yılgör (Fri,) studied this question.