论文标题
legendre $ g $ - 阵列对和几个$ g $ - array家庭的理论统一
Legendre $G$-array pairs and the theoretical unification of several $G$-array families
论文作者
论文摘要
我们调查了Legendre $ g $ - 阵列对与几个不同的完美binary $ g $ array家庭有何关系。特别是我们研究Legendre $ g $ - array对，Sidelnikov-lempel-Cohn-Eastman $ \ Mathbb {Z} _ {Q-1} $ - andares $阵列，Yamada-Pott $ G $ -Array Pairs，Ding-Helleseth-Martinseth-Martinsen $ \ Mathbb $ \ Mathbb { \ Mathbb {z} _p^{m} $ - 数组，Yamada $ \ Mathbb {Z} _ {（Q-1）/2} $ - 阵列，Szekeres $ \ Mathbb {Z}^M _ {Z}^M _ {P} baumert $ \ mathbb {z}^{m_1} _ {p_1} \ times \ times \ mathbb {z}^{m_2} _ {p_2} $ - 数组对。我们的工作还解决了丁〜[j。组合。 des。 16（2008），164-171]。此外，我们提供了一些基于计算机搜索的存在和关于Legendre $ \ Mathbb {z} _n $ array对的不存在的结果。最后，通过使用Cyclotomic Cosets，我们提供了一个以前未知的Legendre $ \ Mathbb {Z} _ {57} $ - 数组对。
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.
