On DNA Codes using the Ring Z4 + wZ4

In this work, we study the DNA codes arising from the ring $R=c{Z}_{4}+w\mathbf{Z}_{4}$, where $w^{2}=2+2w$ 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 $\phi$. 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.

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