On the construction of reversible DNA codes over <i>F</i> <i>42m</i> via <i>T</i>n-set codes

The main objective of this paper is to introduce a new approach for constructing reversible and reversible DNA codes over the finite fields F42m, m >= 1 from any given polynomials by utilizing Tn-set codes. Notably, these polynomials are not required to be self-reciprocal divisors of xn-1. In addition to this method, we provide some results that demonstrate how to generate reversible and reversible DNA codes from any [n, k, d]-cyclic codes over F42m by applying Tn-set codes. Moreover, this approach allows us to determine a lower bound for the distance before completing the entire calculation process. We also construct a correspondence table between DNA sequences made up of 20-bases and all 256 elements of the linear code (Tg5 | T5(g*)degrees 4i over F16, where g = w13 + x + w2x2 + w3x3 is a polynomial in x over F16 and (g*)degrees 4 represents the Hadamard 4th-power of the reciprocal polynomial g* to demonstrate the fact that non-reversible codes may correspond to reversible DNA codes. Additionally, we provide a detailed table presenting some outcomes related to l-MDS codes, self-orthogonal codes, and their associated parameters.