Semidefinite programming bounds for complex spherical codes

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 stabilize...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Wei-Jiun Kao, Suda, Sho, Wei-Hsuan, Yu
Format: Article
Language:English
Subjects:
Codes
Polynomials
Rings (mathematics)
Semidefinite programming
Upper bounds
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422