New Primitive OBZCPs of Lengths up to 49

This paper aims to search for new primitive optimal and sub-optimal Odd Binary Z-Complimentary Pairs (OBZCPs) for lengths up to 49. As an alternative to the celebrated binary Golay complementary pairs, optimal OBZCPs are the best almost-complementary sequence pairs having odd lengths. We introduce a computer search algorithm with complexity O(2N), where N denotes the sequence length and then show optimal results for all 27 ≤ N ≤ 33 and $N=37,41,49$. For those sequence lengths (i.e., $N=35,39,43,45,47$) with no optimal pairs, we show OBZCPs with largest zero-correlation zone (ZCZ) widths (i.e., Z-optimal). Finally, based on the Pursley-Sarwate criterion, we present a table of OBZCPs with smallest demerit factors in terms of the combined auto-correlation and cross-correlation.