Abstract
In this paper we give three constructions of cyclic self-orthogonal codes over \(\mathbb {Z}_{2^k}\), for \(k\ge 3,\) from Boolean functions on n variables. The first construction for each k, \(3\le k\le n,\) yields a self-orthogonal \(\mathbb {Z}_{2^k}\)-code of length \(2^{n+2}\) with all Euclidean weights divisible by \(2^{k+1}.\) In the remaining two constructions, for each even n and \(k\ge 3,\) we generate a self-orthogonal \(\mathbb {Z}_{2^k}\)-code of length \(2^{n+1}.\) All Euclidean weights in the constructed code are divisible by \(2^{2k-1}\) or \(2^{k+1}\), depending on which of the two constructions is used.
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Acknowledgements
This work has been supported by Croatian Science Foundation under the project 6732. The authors would like to thank the reviewers for their careful reading of the manuscript and for their comments that led to an improvement of the exposition.
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This work was supported by Croatian Science Foundation under the project 6732.
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Ban, S., Rukavina, S. Construction of self-orthogonal \(\mathbb {Z}_{2^k}\)-codes. Des. Codes Cryptogr. 92, 1243–1250 (2024). https://doi.org/10.1007/s10623-023-01340-3
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DOI: https://doi.org/10.1007/s10623-023-01340-3