Wieferich pairs and Barker sequences
Wieferich pairs and Barker sequences
复制标题
DOI：
10.1007/s10623-009-9301-3
复制
发表时间：
2009-12
期刊：
影响因子：
--
通讯作者：
Michael J. Mossinghoff
中科院分区：
文献类型：
--
作者：
Michael J. Mossinghoff
证明了如果存在长度n> 13的Barker序列，则eij = 189 260 468 001 034 441 522 766 781 604，orn> 2 · 1030.这将长巴克序列长度的下限提高了107倍以上。我们还证明了除了小于1600个整数n ≤ 4 ·1026之外的所有整数都可以作为循环Hadamard矩阵的阶被消去。这些结果是通过完成广泛的搜索Wieferich素数对（q，p），这是由relationmodp 2定义，并结合一些算术限制n分析他们的结果。
We show that if a Barker sequence of lengthn> 13 exists, then eithern= 189 260 468 001 034 441 522 766 781 604, orn> 2 · 1030. This improves the lower bound on the length of a long Barker sequence by a factor of more than 107. We also show that all but fewer than 1600 integersn≤ 4 · 1026can be eliminated as the order of a circulant Hadamard matrix. These results are obtained by completing extensive searches for Wieferich prime pairs (q,p), which are defined by the relationmodp2, and analyzing their results in combination with a number of arithmetic restrictions onn.