A Computer Search of Primitive OBZCPs of Lengths up to 49
<|reference_start|>A Computer Search of Primitive OBZCPs of Lengths up to 49: This paper aims to search for 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 $O(2^N)$, 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, we present a table of OBZCPs with smallest demerit factors in terms of the combined auto-correlation and cross-correlation.<|reference_end|>
@article{kazakov2024a,
    title={A Computer Search of New OBZCPs of Lengths up to 49},
    author={Peter Kazakov and Zilong Liu},
    journal={arXiv preprint arXiv:2402.06081},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06081},
    primaryClass={cs.IT math.IT math.NT}
}