Abstract
The structures of cyclic DNA codes of odd length over the finite ringsВ R = Z4 + wZ4, w^2 = 2 and S = Z4 + wZ4 + vZ4 + wvZ4; w^2 = 2; v^2 =v; wv = vw are studied. The links between the elements of the rings R, SВ and 16 and 256 codons are established, respectively. The cyclic codes of odd length over the finite ring RВ satisfy reverse complement constraint and the cyclic codes of odd length over the finite ring SВ satisfy reverse constraint and reverse complement constraint are studied. The binary images of the cyclic DNA codes over the finite rings RВ and SВ are determined. Moreover, a family of DNA skew cyclic codes over RВ is constructed, its property of being reverse complement is studied.
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