تقرير
Legendre $G$-array pairs and the theoretical unification of several $G$-array families
| العنوان: | Legendre $G$-array pairs and the theoretical unification of several $G$-array families |
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| المؤلفون: | Arasu, K. T., Bulutoglu, D. A., Hollon, J. R. |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 11T22 |
| الوصف: | We investigate how Legendre $G$-array pairs are related to several different perfect binary $G$-array families. In particular we study the relations between Legendre $G$-array pairs, Sidelnikov-Lempel-Cohn-Eastman $\mathbb{Z}_{q-1}$-arrays, Yamada-Pott $G$-array pairs, Ding-Helleseth-Martinsen $\mathbb{Z}_{2}\times \mathbb{Z}_p^{m}$-arrays, Yamada $\mathbb{Z}_{(q-1)/2}$-arrays, Szekeres $\mathbb{Z}^m_{p}$-array pairs, Paley $\mathbb{Z}^m_{p}$-array pairs, and Baumert $\mathbb{Z}^{m_1}_{p_1}\times \mathbb{Z}^{m_2}_{p_2}$-array pairs. Our work also solves one of the two open problems posed in Ding~[J. Combin. Des. 16 (2008), 164-171]. Moreover, we provide several computer search based existence and non-existence results regarding Legendre $\mathbb{Z}_n$-array pairs. Finally, by using cyclotomic cosets, we provide a previously unknown Legendre $\mathbb{Z}_{57}$-array pair. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2004.05608 |
| رقم الأكسشن: | edsarx.2004.05608 |
| قاعدة البيانات: | arXiv |
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