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A class of balanced binary sequences with two-valued non-zero autocorrelation sum and good crosscorrelation sum

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Abstract

In this paper, we study a class of binary sequences with two-valued non-zero periodic autocorrelation sum and good periodic crosscorrelation sum as well as balanced properties. We make use of the sequences obtained in (No, J. et al., IEEE Trans. Inform. Theory 44(3), 1278-1282 2001) and adopt the extraction method similar to (Lüke, H. IEEE Trans. Inform. Theory 43(1) 1997). The new sequences are proven to be balanced or almost balanced. Based on these correlation and balanced properties, an important application is to construct Hadamard matrices of order \(p+1\) for \(p\equiv 3~(\)mod 4) and \(2p+2\) for \(p\equiv 1~(\)mod 4). Some examples are shown to verify the theoretical results.

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Acknowledgements

This research is financially supported by the National Natural Science Foundation of China No.61771004 and No. 62371094.

Funding

This research is financially supported by the National Natural Science Foundation of China (No.61771004).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, People’s Republic of China

    Shuhui Shen & Xiaojun Zhang

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  1. Shuhui Shen
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  2. Xiaojun Zhang
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Zhang provided the methodology. Shen wrote the main manuscript. All authors did the validation and reviewed the manuscript.

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Correspondence to Xiaojun Zhang.

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Shen, S., Zhang, X. A class of balanced binary sequences with two-valued non-zero autocorrelation sum and good crosscorrelation sum. Cryptogr. Commun. 16, 649–663 (2024). https://doi.org/10.1007/s12095-023-00692-w

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