On DNA Codes Over the Non-Chain Ring ℤ4 +uℤ4 +u2ℤ4 with u3 =1

In this paper, we present a novel design strategy of DNA codes with length 3n over the non-chain ring ℤ
4
+uℤ
4
+u
²
ℤ
4
with 64 elements and u
³
=1, where n denotes the length of a code over R. We first study and analyze a distance conserving map defined over the ring R into the length-3 DNA sequences. Then, we derive some conditions on the generator matrix of a linear code over R, which leads to a DNA code with reversible, reversible-complement, homopolymer 2-run-length, and
3
^w
n
-GC-content constraints for integer w (0 ≤ w ≤ 3n). Finally, we propose a new construction of DNA codes using Reed-Muller type generator matrices. This allows us to obtain DNA codes with reversible, reversible-complement, homopolymer 2-run-length, and -GC-content constraints.