2024/02/08 by Peter Kazakov, Zilong Liu, Kazakov, Peter +1
Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #VLSI and FPGA Design Techniques
paper · pdf · doi:10.48550/arxiv.2402.06081
openalex publication_date 2024/02/08 · openalex created_date 2024/02/13 · openalex updated_date 2026/07/28
This paper aims to search for new 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 time 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 (PSC), we present a table of OBZCPs with smallest combined auto-correlation and cross-correlation.