Complex Spherical Designs and Codes
Complex Spherical Designs and Codes
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DOI：
10.1002/jcd.21379
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发表时间：
2011-04
影响因子：
0.7
通讯作者：
Aidan Roy;Sho Suda
中科院分区：
文献类型：
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作者：
Aidan Roy;Sho Suda
当Delsarte，Goethals和Seidel显示了真正的球形设计和真实且复杂的投影设计，当设计的强度很高时，与该代码的程度相比，在设计的强度很高时产生了关联方案。相比之下，尽管在众多应用中，尽管它们在许多应用中的重要性，但在复杂单元球体上的设计仍然相对未经评价。在本文中，我们开发了复杂的球形设计的概念，并显示了有多少此类设计具有关联方案的结构。与真实的球形设计和实际且复杂的投影设计相反，这些关联方案是非对称的。
Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast, designs on the complex unit sphere remain relatively uninvestigated, despite their importance in numerous applications. In this paper, we develop the notion of a complex spherical design and show how many such designs carry the structure of an association scheme. In contrast with the real spherical designs and the real and complex projective designs, these association schemes are nonsymmetric.