Coherent configurations and triply regular association schemes obtained from spherical designs
Coherent configurations and triply regular association schemes obtained from spherical designs
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DOI：
10.1016/j.jcta.2010.03.016
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发表时间：
2009-03
期刊：
影响因子：
--
通讯作者：
Sho Suda
中科院分区：
文献类型：
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作者：
Sho Suda
Delsarte、Goethals和Seidel证明了如果X是一个球面t-设计，且次数s满足t <$2s −2，则X具有一个结合方案的结构。Bannai和Bannai还证明了，如果X是次数s满足t=2s−3的对映球面t-设计，则同样的结论也成立。作为这些结果的推广，我们证明了具有一定性质的球形设计的并集具有相干配置的结构。我们得到了紧球面4-、5-、7-设计、互无偏基、带参数对称设计的联结系统的三重正则性。
Delsarte, Goethals and Seidel showed that if X is a spherical t-design with degree s satisfying t⩾2s−2, X carries the structure of an association scheme. Also Bannai and Bannai showed that the same conclusion holds if X is an antipodal spherical t-design with degree s satisfying t=2s−3. As a generalization of these results, we prove that a union of spherical designs with a certain property carries the structure of a coherent configuration. We derive triple regularity of tight spherical 4-, 5-, 7-designs, mutually unbiased bases, linked systems of symmetric designs with certain parameters.