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arXiv · 2204.04108

Semidefinite programming bounds for complex spherical codes

Wei-Jiun Kao·Sho Suda·Wei-Hsuan Yu
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Abstract

A complex spherical code is a finite subset on the unit sphere in $\mathbb{C}^d$. A fundamental problem on complex spherical codes is to find upper bounds for those with prescribed inner products. In this paper, we determine the irreducible decomposition under the action of the one-point stabilizer of the unitary group $U(d)$ on the polynomial ring $\mathbb{C}[z_1\ldots,z_d,\bar{z}_1,\ldots,\bar{z}_d]$ in order to obtain the semidefinite programming bounds for complex spherical codes.

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Wei-Jiun Kao, Sho Suda, Wei-Hsuan Yu. 2022-04-08. Semidefinite programming bounds for complex spherical codes. https://arxiv.org/abs/2204.04108

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