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Cyclic codes over \({\mathbb {F}}_2 +u{\mathbb {F}}_2+v{\mathbb {F}}_2 +v^2 {\mathbb {F}}_2 \) with respect to the homogeneous weight and their applications to DNA codes

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In this paper, we study cyclic codes and their duals over the local Frobenius non-chain ring \(R={\mathbb {F}}_2[u,v] / \langle u^2=v^2,uv \rangle \), and we obtain optimal binary linear codes with respect to the homogeneous weight over R via a Gray map. Moreover, we characterize DNA codes as images of cyclic codes over R.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Yıldız Technical University, 34220, Esenler, Istanbul, Turkey

    Merve Bulut Yılgör, Fatmanur Gürsoy & Fatih Demirkale

  2. Department of Mathematics, Karamanoğlu Mehmetbey University, Karaman, Turkey

    Elif Segah Öztaş

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  1. Merve Bulut Yılgör
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  2. Fatmanur Gürsoy
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  3. Elif Segah Öztaş
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  4. Fatih Demirkale
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Correspondence to Merve Bulut Yılgör.

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Bulut Yılgör, M., Gürsoy, F., Öztaş, E.S. et al. Cyclic codes over \({\mathbb {F}}_2 +u{\mathbb {F}}_2+v{\mathbb {F}}_2 +v^2 {\mathbb {F}}_2 \) with respect to the homogeneous weight and their applications to DNA codes. AAECC 32, 621–636 (2021). https://doi.org/10.1007/s00200-020-00416-0

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