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On cyclic DNA codes over the rings Z_{4}+wZ_{4} and Z_{4}+wZ_{4}+vZ_{4}+wvZ_{4} (1605.02968v1)
Published 25 Mar 2016 in cs.IT and math.IT
Abstract: The structures of cyclic DNA codes of odd length over the finite rings R=Z_{4}+wZ_{4}, w{2}=2 and S=Z_{4}+wZ_{4}+vZ_{4}+wvZ_{4},w{2}=2,v{2}=v,wv=vw are studied. The links between the elements of the rings R, S and 16 and 256 codons are established, respectively. Cyclic codes of odd length over the finite ring R satisfies reverse complement constraint and cyclic codes of odd length over the finite ring S satisfy reverse constraint and reverse complement constraint are studied. Binary images of the cyclic DNA codes over the finite rings R and S are determined. Moreover, a family of DNA skew cyclic codes over R is constructed, its property of being reverse complement is studied.