A Matrix-Theoretic Approach to the Construction of Reversible DNA Codes Over F₄<SUP>2</SUP>t

Let n,k , and t be the positive integers. The primary aim of this paper is to introduce a new approach for the construction of reversible and reversible DNA codes using the concept of double-reflected matrices of any matrices over a commutative ring with unity R and the finite field F-4(2t) , respectively. The key benefit of our research is that we can generate reversible and reversible DNA codes using any kx n matrix with rank k. Moreover, this approach enables the determination of a lower bound for the distance before completing the whole calculation process. We also provide a detailed table presenting some outcomes related to MDS codes, AMDS codes and their associated parameters. Additionally, we include several examples to illustrate our constructions. In the last example, we construct a correspondence table between DNA sequences of length 20 and all 256 elements of the linear code C over F-16 to demonstrate that non-reversible codes may correspond to reversible DNA codes.