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Z-complementary pairs with flexible lengths and large zero odd-periodic correlation zones

  • * Corresponding author: Yong Wang

    * Corresponding author: Yong Wang 
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  • Z-complementary pairs (ZCPs) have been widely used in different communication systems. In this paper, we first investigate the odd-periodic correlation property of ZCPs, and propose a new class of ZCPs, called ZOC-ZCPs with zero correlation zone (ZCZ) width $ Z $ and zero odd-period correlation zone (ZOCZ) width $ Z_{odd} = Z $ by horizontal concatenation of a certain combination of some known ZCPs. Particularly, based on any known Golay pair, we can generate a class of GCPs of more flexible length whose ZOCZ width is larger than a quarter of the sequence length.

    Mathematics Subject Classification: Primary: 94A05; Secondary: 60G35.

    Citation:

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  • Figure 1.  The odd-periodic correlation magnitudes of ZCP in Example 1

    Figure 2.  The odd-periodic correlation magnitudes of a GCP in Example 2

    Table 1.  The Parameters of Some ZCPs by Construction 1

    $ Sequence\; Length $ $ ZCZ\; width $ $ ZOCZ\; width $
    $ 4(2^{m+1}+2^m) $ $ 2^{m+1} $ $ 2^{m+1} $
    $ 4(2^m+1) $ $ 2^{m-1}+1 $ $ 2^{m-1}+1 $
    $ 4(2^m-1) $ $ 2^{m-1} $ $ 2^{m-1} $
    $ 4(2^{m+3}+2^{m+2}+2^{m+1} $) $ 2^{m+3} $ $ 2^{m+3} $
    $ 56\cdot 2^{\alpha}10^{\beta}26^{\gamma} $ $ 12\cdot 2^{\alpha}10^{\beta}26^{\gamma} $ $ 12\cdot 2^{\alpha}10^{\beta}26^{\gamma} $
    $ 48 \cdot 2^{\alpha}10^{\beta}26^{\gamma} $ $ 10\cdot 2^{\alpha}10^{\beta}26^{\gamma} $ $ 10\cdot 2^{\alpha}10^{\beta}26^{\gamma} $
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