Application of (σ,δ)-cyclic codes in DNA codes over a non-chain ring

For a prime Formula: see text and a positive integer Formula: see text, let Formula: see text be the finite field of characteristic Formula: see text, and Formula: see text be a non-chain ring for a positive integer Formula: see text. In this paper, we study the Formula: see text-cyclic codes over Formula: see text. Further, we study the application of these codes in finding DNA codes. Toward this, we first define a Gray map to find classical codes over Formula: see text using codes over the ring Formula: see text. Later, we find the conditions for a Formula: see text-cyclic code to be reversible. Finally, we provide DNA codes using this algebraic method with some classical codes of better parameters.