On optimal binary Z-complementary pair of odd period

In this paper we introduce the optimal odd-period binary Z-complementary pairs (OB-ZCPs), which display properties similar to Golay complementary pairs. These pairs have the maximum possible zero-correlation-zone (ZCZ) of width (N + 1)/2, where N denotes the sequence length, and the minimum possible magnitude of 2 for each out-of-zone aperiodic auto-correlation sum. Furthermore, we show that the optimal OB-ZCPs correspond to sets of almost difference families and present some of their interesting properties.