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Self-dual constacyclic codes of length \(2^s\) over the ring \(\mathbb {F}_{2^m}[u,v]/\langle u^2, v^2, uv-vu \rangle \)

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Abstract

In this paper, we classify all self-dual \(\lambda \)-constacyclic codes of length \(2^s\) over the finite commutative local ring \(R_{u^2, v^2,2^m}=\mathbb {F}_{2^m}[u,v]/\langle u^2, v^2, uv-vu \rangle \) corresponding to units of the forms \(\lambda =\alpha +\gamma v+\delta uv\), \(\alpha +\beta u+\delta uv\), \(\alpha +\beta u+\gamma v+\delta uv\), where \(\alpha ,\beta ,\gamma \in \mathbb {F}^*_{2^m}\) and \(\delta \in \mathbb {F}_{2^m}\). Moreover, the Hamming distance of these \(\lambda \)-constacyclic codes are completely determined.

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Acknowledgements

We would like to thank the reviewers for their your valuable comments and suggestions. P.K. Kewat gratefully acknowledges the Department of Science and Technology-Science and Energy Research Board (DST-SERB, India, Grant No. YSS/2015/001801) for financial assistance. This paper was supported in part by the Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University.

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Authors and Affiliations

  1. Departmaent of Mathematical Science, Kent State University, 4314 Mahoning Avenue, Warren, OH, 44483, USA

    Hai Q. Dinh

  2. Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826 004, India

    Pramod Kumar Kewat & Sarika Kushwaha

  3. Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai, 52000, Thailand

    Woraphon Yamaka

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  1. Hai Q. Dinh
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  2. Pramod Kumar Kewat
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  3. Sarika Kushwaha
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  4. Woraphon Yamaka
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Dinh, H.Q., Kewat, P.K., Kushwaha, S. et al. Self-dual constacyclic codes of length \(2^s\) over the ring \(\mathbb {F}_{2^m}[u,v]/\langle u^2, v^2, uv-vu \rangle \). J. Appl. Math. Comput. 68, 431–459 (2022). https://doi.org/10.1007/s12190-021-01526-9

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