On DNA Codes Over the Non-Chain Ring ℤ_4+uℤ_4+u^2ℤ_4 with u^3=1
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In this paper, we present a novel design strategy of DNA codes with length 3n over the non-chain ring R=ℤ_4+uℤ_4+u^2ℤ_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 w/3n-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 2/3-GC-content constraints.
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