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Reversible cyclic codes over some finite rings and their application to DNA codes

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Abstract

For a prime p and \(q=p^{m}\), we study reversible cyclic codes of arbitrary length over a ring \( R = \mathbb {F}_q + u \mathbb {F}_q\) where \(u^2=0 ~\mathrm{{mod}}~q\). First, we find a unique set of generators for cyclic codes over R followed by a classification of reversible cyclic codes concerning their generators. Further, we find the set of generators for dual codes, and then under certain conditions, it is shown that dual of reversible cyclic code over \(\mathbb {Z}_2+u\mathbb {Z}_2\) is reversible. Moreover, we discuss reversible-complement cyclic codes over \(\mathbb {F}_8+u\mathbb {F}_8\), which play a very significant role in DNA computing. Finally, to show the importance of these results, examples of reversible cyclic codes and DNA codes are provided.

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Acknowledgements

The authors are thankful to the Department of Science and Technology (DST)(Ref No. DST /INSPIRE/03/2016/001445) and Indian Institute of Technology Patna, Govt. of India, for providing financial support and research facilities.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Patna, Bihta, Patna, 801 106, India

    Om Prakash, Shikha Patel & Shikha Yadav

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  1. Om Prakash
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  2. Shikha Patel
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  3. Shikha Yadav
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Correspondence to Om Prakash.

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Communicated by Thomas Aaron Gulliver.

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Prakash, O., Patel, S. & Yadav, S. Reversible cyclic codes over some finite rings and their application to DNA codes. Comp. Appl. Math. 40, 242 (2021). https://doi.org/10.1007/s40314-021-01635-y

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  • DOI: https://doi.org/10.1007/s40314-021-01635-y

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