A matrix-theoretic approach to the construction of reversible DNA codes over F 4 2 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 R and the finite field F 4 2 t , respectively. The key benefit of our research is that we can generate reversible and reversible DNA codes using any k × 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.