A Computer Search of New OBZCPs of Lengths up to 49

Abstract

In this article, we aim to search for new optimal and suboptimal odd binary Z-complementary 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 time complexity $O(2^{N})$, where $N$ denotes the sequence length and then show optimal results for all $27 \leq N \leq 33$ 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 widths (i.e., $Z$-optimal). Finally, based on the Pursley–Sarwate criterion, we present a table of OBZCPs with smallest combined auto-correlation and cross-correlation.