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arXiv · 2402.06081

A Computer Search of New OBZCPs of Lengths up to 49

Peter Kazakov·Zilong Liu
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Abstract

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 $O(2^N)$, where $N$ denotes the sequence length and then show optimal results for all $27 \le N \le 33$ 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.

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Peter Kazakov, Zilong Liu. 2024-11-13. A Computer Search of New OBZCPs of Lengths up to 49. https://arxiv.org/abs/2402.06081

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