On Even-Period Binary Z-Complementary Pairs with Large ZCZs

Abstract

For an even-period binary Z-complementary pair (EB-ZCP), if it is not a Golay complementary pair (GCP), we show that Z ≤ N-2, where N and Z denote the sequence length and the zero correlation zone (ZCZ) width, respectively. This result partially answers the Fan-Yuan-Tu conjecture in 2007. In addition, we present a construction of EB-ZCPs with large ZCZ widths, where N=2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m+1</sup> +2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> and Z=2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m+1</sup> . Interestingly, each of the proposed EB-ZCPs features zero out-of-phase aperiodic auto-correlation sums except for the time-shift of ±2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m+1</sup> , thus displaying a very close correlation property to that of GCPs.