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    Reversible codes and applications to DNA codes over (F42t[u]/(u2 - 1)
    (American Institute of Mathematical Sciences, 2023) Alsuraiheed, Turki; Öztaş, Elif Segah; Ali, Shakir; Yılgör, Merve Bulut
    Let n ≥ 1 be a fixed integer. Within this study, we present a novel approach for discovering reversible codes over rings, leveraging the concept of r-glifted polynomials. This technique allows us to achieve optimal reversible codes. As we extend our methodology to the domain of DNA codes, we establish a correspondence between 4t-bases of DNA and elements within the ring (formula presented). By employing a variant of r-glifted polynomials, we successfully address the challenges of reversibility and complementarity in DNA codes over this specific ring. Moreover, we are able to generate reversible and reversible-complement DNA codes that transcend the limitations of being linear cyclic codes generated by a factor of xn − 1.