论文标题
第四纪legendre对
Quaternary Legendre Pairs
论文作者
论文摘要
我们介绍了第四纪的legendre对长度$ \ ell $。与二进制Legendre对相反，它们也可以以$ \ ell $的形式存在。首先，我们证明它们与订单$ 2 \ ell+2 $的第四纪hadamard矩阵以及二进制Hadamard订单矩阵的构建相关，$ 4 \ ell+4 $。然后，对于Prime $ p> 2 $，我们提供了一对长度$ p $的构造，我们可以从中得出第四纪的legendre对长度$ \ ell = 2p $ by Decompression，以$ p = 3,5,5,7,13,19,19,31,41 $。此外，我们还为所有剩余的$ \ ell \ le \ le 24 $提供了Legendre对长度$ \ ell $的构造。
We introduce quaternary Legendre pairs of length $\ell$. In contrast to binary Legendre pairs they can exist for even $\ell$ as well. First we show that they are pertinent to the construction of quaternary Hadamard matrices of order $2\ell+2$ and thus of binary Hadamard matrices of order $4\ell+4$. Then for a prime $p>2$ we present a construction of a pair of sequences of length $p$ from which we can derive quaternary Legendre pairs of length $\ell=2p$ by decompression for $p=3,5,7,13,19,31,41$. Moreover, we give also constructions of Legendre pairs of length $\ell$ for all remaining even $\ell\le 24$.
