(θi, λ)-constacyclic codes and DNA codes over Z4

In 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.