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.