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Two infinite families of two-weight codes over \(\mathbb {Z}_{2^m}\)

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Abstract

In this paper, we first construct two infinite families of new two-weight codes over \(\mathbb {Z}_{2^m}\) with respect to homogeneous metric and Lee metric by their generator matrices, which generalizes the results in Shi et al (Des Codes Cryptogr 88(3):1–13, 2020) from two different directions. We construct some optimal codes over \(\mathbb {Z}_{2^m}\) and prove all codes in one of these two families are self-orthogonal. Finally, we determine the linearity of the Gray images of the codes we constructed for Lee metric completely.

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Acknowledgements

The authors would like to thank Dr. R. Wu for helpful discussions.

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  1. Shitao Li and Minjia Shi are with School of Mathematical Sciences, Anhui University, Hefei, China

    Shitao Li & Minjia Shi

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  1. Shitao Li
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  2. Minjia Shi
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Correspondence to Minjia Shi.

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This research is supported by the National Natural Science Foundation of China (12071001) and 2021 University Graduate Research Project (Y020410077).

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Li, S., Shi, M. Two infinite families of two-weight codes over \(\mathbb {Z}_{2^m}\). J. Appl. Math. Comput. 69, 201–218 (2023). https://doi.org/10.1007/s12190-022-01736-9

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  • DOI: https://doi.org/10.1007/s12190-022-01736-9

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