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

• * Corresponding author: Yong Wang
• 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:

• 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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