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Codes over \(F_{4}+vF_4\) and some DNA applications

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Abstract

In this work, we study the structure of linear, constacyclic and cyclic codes over the ring \(R=F_{4}[v]/(v^{2}-v)\) and establish relations to codes over \( F_{4}\) by defining a Gray map between R and \(F_{4}^{2}\) where \(F_4\) is the field with 4 elements. Constacyclic codes over R are shown to be principal ideals. Further, we study skew constacyclic codes over R. The structure of all skew constacyclic codes is completely determined. Furthermore, we introduce reversible codes which provide a rich source for DNA codes. We conclude the paper by obtaining some DNA codes over R that attain the Griesmer bound.

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Acknowledgments

The authors wish to express sincere thanks to the anonymous referees who gave many helpful comments and suggestions that greatly improved the presentation of the paper. This paper is presented in The 4th International Congress on Mathematical Software 2014 (ICMS 2014) and partially published in the proceedings [5].

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Authors and Affiliations

  1. Department of Mathematics, Yildiz Technical University, Istanbul, Turkey

    Aysegul Bayram, Elif Segah Oztas & Irfan Siap

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  1. Aysegul Bayram
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  2. Elif Segah Oztas
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  3. Irfan Siap
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Correspondence to Irfan Siap.

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Communicated by J.-L. Kim.

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Bayram, A., Oztas, E.S. & Siap, I. Codes over \(F_{4}+vF_4\) and some DNA applications. Des. Codes Cryptogr. 80, 379–393 (2016). https://doi.org/10.1007/s10623-015-0100-8

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  • DOI: https://doi.org/10.1007/s10623-015-0100-8

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