Abstract
Classically, negacyclic codes over finite fields enjoy a good error-correcting capability with respect to the Lee metric. Lee distance of negacyclic codes of length \(2^s\) over the finite commutative chain ring \({\mathbb {Z}}_{2^e}\) have been determined. Further, these results have been generalized to the class of \((4z-1)\)-constacyclic codes of length \(2^s\) over \({{\,\textrm{GR}\,}}\left( 2^e,m\right) \), \(z\in {{\,\textrm{GR}\,}}\left( 2^e,m\right) \). In this paper, we obtain the Lee distance of a more general class of \(\left( 1+2\sigma _1+4z\right) \)-constacyclic codes of length \(2^s\) over \({{\,\textrm{GR}\,}}\left( 2^e,m\right) \), where \(\sigma _1 \in {\mathcal {T}}\left( 2,m\right) \smallsetminus \{0\}\) and \(z \in {{\,\textrm{GR}\,}}\left( 2^e,m\right) \). As an application, we compute all maximum distance separable (MDS) codes with respect to the Lee distance.
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Acknowledgements
We would like to thank the reviewers for their valuable comments and suggestions. The second and the third authors gratefully acknowledge the Department of Science and Technology-Science and Energy Research Board (DST-SERB, India, Grant No. YSS/2015/001801) for financial assistance.
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Dinh, H.Q., Kewat, P.K. & Mondal, N.K. Lee distance distribution of repeated-root constacyclic codes over \(\hbox {GR}\left( 2^e,m\right) \) and related MDS codes. J. Appl. Math. Comput. 68, 3861–3872 (2022). https://doi.org/10.1007/s12190-021-01694-8
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DOI: https://doi.org/10.1007/s12190-021-01694-8