Abstract
We determine the possible homogeneous weights of regular projective two-weight codes over \(\mathbb {Z}_{2^k}\) of length \(n>3\), with dual Krotov distance \(d^{\lozenge }\) at least four. The determination of the weights is based on parameter restrictions for strongly regular graphs applied to the coset graph of the dual code. When \(k=2\), we characterize the parameters of such codes as those of the inverse Gray images of \(\mathbb {Z}_4\)-linear Hadamard codes, which have been characterized by their types by several authors.
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Acknowledgements
The authors are grateful to the anonymous referees for helpful remarks. This research is supported by National Natural Science Foundation of China (61672036), the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2015D11), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (05015133) and Key projects of support program for outstanding young talents in Colleges and Universities (gxyqZD2016008).
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Communicated by J. H. Koolen.
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Shi, M., Sepasdar, Z., Alahmadi, A. et al. On two-weight \(\mathbb {Z}_{2^k}\)-codes. Des. Codes Cryptogr. 86, 1201–1209 (2018). https://doi.org/10.1007/s10623-017-0390-0
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DOI: https://doi.org/10.1007/s10623-017-0390-0