On DNA Codes using the Ring Z4 + wZ4

In this work, we study the DNA codes arising from the ring R=cZ₄+wZ₄, where w²=2+2w with 16 elements. We establish a one to one correspondence, between the elements of the ring R and all the DNA words of length 2, by defining a distance preserving Gau map φ. Using this map, we give several new classes of DNA codes which are reversible and reversible-complement. We also give general conditions on the generator matrix of a code over R which produces DNA codes with the required properties using the Gau map. Some of the constructed DNA codes are optimal.