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Constructions of two-dimensional Z-complementary array pairs with large ZCZ ratio

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Abstract

Two-dimensional (2-D) Z-complementary array pair (ZCAP) is a pair of 2-D arrays, whose 2-D autocorrelation sum gives zero value at all time shifts in a zone around the (0, 0) time shift, except the (0, 0) time shift. The zone is called a zero correlation zone (ZCZ). 2-D ZCAPs include 2-D Golay complementary array pairs (GCAPs) as special cases, and can be applicable in 2-D synchronization. In this paper, we focus on designing new 2-D ZCAPs by exploring two promising approaches. The first construction of 2-D ZCAPs uses 1-D ZCPs as the initial stage, such that any binary ZCP and q-phase ZCP can produce a q-phase 2-D ZCAP. The second construction of 2-D ZCAPs is based on 2-D generalized Boolean functions (GBFs), and the resulting 2-D ZCAPs can have the largest 2-D ZCZ ratio 6/7, compared with known 2-D ZCAPs but not 2-D GCAPs in the literature. Here the ZCZ ratio is defined as the ratio of the ZCZ size over the array size.

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Acknowledgements

The authors are very grateful to the anonymous reviewers and the Associate Editor for their valuable comments that highly improved the presentation and quality of this paper. This work was supported by National Natural Science Foundation of China under Grants 11971395 and also by the Central Government Funds for Guiding Local Scientific and Technological Development under Grant 2021ZYD0001.

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Hui Zhang & Cuiling Fan

  2. Department of Mathematics, University of Paris VIII, 93526, Saint-Denis, France

    Sihem Mesnager

  3. University Sorbonne Paris Cité, Laboratory Analysis, Geometry and Applications (LAGA), UMR 7539, CNRS, 93430, Villetaneuse, France

    Sihem Mesnager

  4. Telecom Paris, Polytechnic Institute of Paris, 91120, Palaiseau, France

    Sihem Mesnager

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  1. Hui Zhang
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  2. Cuiling Fan
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Correspondence to Cuiling Fan.

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Communicated by J. Jedwab.

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Zhang, H., Fan, C. & Mesnager, S. Constructions of two-dimensional Z-complementary array pairs with large ZCZ ratio. Des. Codes Cryptogr. 90, 1221–1239 (2022). https://doi.org/10.1007/s10623-022-01035-1

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  • DOI: https://doi.org/10.1007/s10623-022-01035-1

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