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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.06081 |
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| _version_ | 1866929589361573888 |
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| author | Kazakov, Peter Liu, Zilong |
| author_facet | Kazakov, Peter Liu, Zilong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Computer Search of New OBZCPs of Lengths up to 49 Kazakov, Peter Liu, Zilong Information Theory Number Theory 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. |
| title | A Computer Search of New OBZCPs of Lengths up to 49 |
| topic | Information Theory Number Theory |
| url | https://arxiv.org/abs/2402.06081 |