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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.

- Abdullah Dertli
- 2011

We construct MacDonald codes over the ring F 2 +vF 2 , where v 2 = v, F 2 = {0, 1}. We also investigate some of their properties.

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)

We construct a new Gray map from S n to F 3n 2 where S = F 2 +uF 2 +u 2 F 2 , u 3 = 1. It is both an isometry and a weight preserving map. It was shown that the Gray image of cyclic code over S is quasi-cyclic codes of index 3 and the Gray image of quasi-cyclic code over S is l-quasi-cyclic code of index 3. Moreover, the skew cyclic and skew quasi-cyclic… (More)

—In this paper, we study the structure of cyclic, quasi cyclic, constacyclic codes and their skew codes over the finite ring R. 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 its dual has been… (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)

In this paper, it was constructed quantum codes from cyclic codes over finite ring S = F 2 + uF 2 + vF 2 , u 2 = u, v 2 = v, uv = vu = 0 for arbitrary length n. It was given a new Gray map Ψ which is both an isometry and weight preserving map. It was shown that C is self orthogonal codes over S, so is Ψ(C). It was given a necessary and sufficient condition… (More)

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