DNA Codes over a Non-chain Ring

We study the algebraic structure of DNA codes constructed over the ring R=F_2 [u,v,w] ⟨u^2=v^2,uv=0,w^2=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.