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- Yasemin Cengellenmis, Abdullah Dertli, Steven T. Dougherty
- Des. Codes Cryptography
- 2014

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)

Copyright c © 2015 Abdullah Dertli, Yasemin Cengellenmis and Senol Eren. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract A method to obtain self orthogonal codes over finite field F2… (More)

We construct MacDonald codes over the ring F2+vF2, where v2 = v, F2 = {0, 1}. We also investigate some of their properties. Mathematics Subject Classification: 94B05

- Abdullah Dertli, Yasemin Cengellenmis, Senol Eren
- ArXiv
- 2014

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

- Abdullah Dertli, Yasemin Cengellenmis
- ArXiv
- 2016

The structures of cyclic DNA codes of odd length over the finite rings R = Z4 + wZ4, w 2 = 2 and S = Z4 + wZ4 + vZ4 + wvZ4, w 2 = 2, v = 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)

- Abdullah Dertli, Yasemin Cengellenmis, Senol Eren
- Discrete Math., Alg. and Appl.
- 2016

Some results are generalized on linear codes over Z3[v]/〈v3 − v〉 in [15] to the ring Rp = Zp[v]/〈vp − v〉, where p is an odd prime number. The Gray images of cyclic and quasi-cyclic codes over Rp are obtained. The parameters of quantum error correcting codes are obtained from negacyclic codes over Rp. A nontrivial automorphism θp on the ring Rp is… (More)

We construct a new Gray map from S to F 3n 2 where S = F2+uF2+uF2, u3 = 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 codes over S… (More)

- Abdullah Dertli, Yasemin Cengellenmis, Senol Eren
- ArXiv
- 2015

In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R = Z3+vZ3+v 2 Z3, v 3 = v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasicyclic 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 = F2 + uF2 + vF2, u2 = u, v2 = 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 for… (More)

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