New Optimal Binary Z-Complementary Pairs of Odd Length $2^m+3$

A pair of sequences is called odd-length binary Z-complementary pair (OB-ZCP) if it is of odd-length and has zero aperiodic autocorrelation sums (AACSs) for all time-shifts within a certain region around the in-phase position, commonly known as zero correlation zone (ZCZ). There are two types of OB-ZCPs, namely Type-I OB-ZCPs and Type-II OB-ZCPs. Type-I OB-ZCPs have ZCZ around the in-phase position. Type-II OB-ZCPs have the ZCZ around the end-shift position. An OB-ZCP (Type-I or Type-II) of odd-length N is called Z-optimal if it achieves a maximum ZCZ width of (N + 1)/2. To date, a systematic construction of Type-II Z-optimal OB-ZCPs exist only for very limited lengths of the form 2^m ± 1, where m is a positive integer. It employs insertion method and delete method on binary Golay complementary pairs (GCPs) of length 2^m derived from second order Reed-Muller codes. In this article, based on iterative insertion method, we construct Type-II Z-optimal OB-ZCPs of lengths 2^m + 3.