Uzekmek, Fatma ZehraÖztaş, Elif SegahÖzen, Mehmet2025-01-122025-01-1220242473-6988https://doi.org/10.3934/math.20241355https://hdl.handle.net/11492/10402In this paper, three new automorphisms were identified over the ring Z(4)+uZ(4)+u(2)Z(4) where u(3 )= u(2). With the help of these automorphisms, the characteristic structures of the generator polynomials for the theta i-cyclic codes and (theta(i),lambda)-constacyclic codes of odd length on this ring were investigated. Also, for all the units over the ring, Z(4)-images of theta i-cyclic and (theta(i),lambda)-constacyclic codes were reviewed with the associated codes based on determined transformations. Using these observations, new and optimal codes were obtained and presented in the table. In addition, a new transformation was identified that involved DNA base pairs with the elements of Z(4). Moreover, a unit reverse polynomial was created, and in this way a new generation method has been built to construct reversible DNA codes over this ring. Finally, this article was further enhanced with supporting examples of the DNA as a part of the study.enCodes Over RingsConstacyclic CodesSkew CodesDNA CodesArticle9102790827929info:eu-repo/semantics/openAccess2-s2.0-85205948621WOS:00132924210000610.3934/math.20241355Q1N/A