Semidefinite programming bounds for complex spherical codes

2022/04/08 by Wei-Jiun Kao, Kao, Wei-Jiun, Sho Suda +3
Engineering · Immunology and Microbiology · #Advanced Wireless Network Optimization #Combinatorics (math.CO) #FOS: Mathematics #Macrophage Migration Inhibitory Factor

paper · pdf · doi:10.48550/arxiv.2204.04108

openalex publication_date 2022/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A complex spherical code is a finite subset on the unit sphere in 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 ℂ[z₁…,z_d,z₁,…,z_d] in order to obtain the semidefinite programming bounds for complex spherical codes.

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