Wieferich pairs and Barker sequences |
| |
Authors: | Michael J Mossinghoff |
| |
Institution: | (1) Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada;(2) Department of Informatics, High Technology Center in Bergen, University of Bergen, Bergen, 5020, Norway |
| |
Abstract: | We show that if a Barker sequence of length n > 13 exists, then either n = 189 260 468 001 034 441 522 766 781 604, or n > 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 integers n ≤ 4 · 1026 can 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 relation qp-1 o 1{q^{p-1} \equiv1} mod p
2, and analyzing their results in combination with a number of arithmetic restrictions on n. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|