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A new Gray map which is both an isometry and a weight preserving map from R = F2 + vF2 + v 2 F2 to F 3 2 is defined. A construction for quantum error correcting codes from cyclic codes over finite ring R = F2 + vF2 + v 2 F2, v 3 = v is given.The parameters of quantum codes which are obtained from cyclic codes over R are determined.

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… (More)

In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R=Z_3+vZ_3+v^2Z_3, v^3=v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains… (More)

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