In this paper, we present a novel design strategy of DNA codes with length
3n over the non-chain ring R=Z4β+uZ4β+u2Z4β
with 64 elements and u3=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
3nwβ-GC-content constraints for integer w (0β€wβ€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 32β-GC-content
constraints.Comment: This paper has been presented in IEEE Information Theory Workshop
(ITW) 2022, Mumbai, INDI