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In this paper, we study the theory for constructing DNA cyclic codes of oddlength over $\Z_4[u]/\langle u^2 \rangle$ which play an important role in DNAcomputing. Cyclic codes of odd length over $\Z_4 + u \Z_4$ satisfy the reverseconstraint and the reverse-complement constraint are studied in this paper. Thestructure and existence of such codes are also studied. The paper concludeswith some DNA example obtained via the family of cyclic codes.

On cyclic DNA codes over the Ring $\Z_4 + u \Z_4$