On the existence of cyclic difference sets with small parameters
On the existence of cyclic difference sets with small parameters
复制标题
关于小参数循环差集的存在性
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
D. M. Gordon
中科院分区：
文献类型：
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作者：
L. D. Baumert;D. M. Gordon
Baumert、洛佩斯和Sanchez之前的研究已经解决了k <= 150的循环（v，k，lambda）差集的存在性，除了六个开放的情况。在本文中，我们表明，其中四个差集不存在。我们还研究了k <= 300的差集和v <= 10，000的循环Hadamard差集的存在性。最后，我们扩展了第二作者的早期搜索，表明不存在非素数幂阶数高达20亿的循环射影平面。
Previous surveys by Baumert and Lopez and Sanchez have resolved the existence of cyclic (v,k,lambda) difference sets with k <= 150, except for six open cases. In this paper we show that four of those difference sets do not exist. We also look at the existence of difference sets with k <= 300 and cyclic Hadamard difference sets with v <= 10,000. Finally, we extend an earlier search of the second author to show that no cyclic projective planes exist with non-prime power orders up to two billion.