DNA codes over groups

The article 'DNA Codes over Groups' delves into the application of DNA for computing and data storage, with a particular focus on the design of DNA codes over groups. It begins by recounting the historical context, including Adleman's pioneering experiment using DNA to solve the traveling salesman problem and the subsequent use of DNA codes to break cryptosystems. The article then introduces the basic properties of DNA strands and their potential for stable, long-term data storage. The main challenge addressed is the need for effective methods to design DNA codes for DNA computing. The paper explores the use of reversible complement cyclic codes over finite rings and fields, highlighting the importance of finding bijections that maintain the desired properties. The article also provides conditions for the existence of compatible functions between groups and DNA codewords, with a focus on groups that can be identified with k-tuples of nucleotides. Additionally, it determines the algebraic structure of DNA codes and presents examples to illustrate the main results. The paper concludes with a discussion on the need for further characterization of groups with automorphisms of order two that meet specific conditions, as well as the invariant subgroups under these automorphisms.