Constructing DNA Codes with Larger Distance from Quaternary Words

In this work, we propose a novel method to construct DNA codes from quaternary words. The method uses permutation groups that act in the set {1, 2, …, 4n}, representing the coordinate and coordinate value of quaternary words. The DNA code is obtained by finding a clique of the construction graph and mapping it using the bijective map 0 → A, 1 → C, 2 → T, 3 → G. We present a new approach to construct DNA codes with larger Hamming distance and reverse-complement distance compared to previously obtained DNA codes. This is achieved by using a modified construction graph tailored to the desired distance parameter. As a result, we can refine a DNA code to have improved Hamming distance and reverse-complement distance while maintaining the fixed GC-content constraint. This method simplifies the search for DNA codes with large distance parameters.