A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4

Takayuki Okuda; Wei Hsuan Yu

doi:10.1016/j.ejc.2015.11.003

A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4

Takayuki Okuda, Wei Hsuan Yu

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

17 引文斯高帕斯（Scopus）

摘要

We give a new upper bound for the cardinality of a set of equiangular lines in Rn with a fixed common angle θ for each (n, θ) satisfying certain conditions. Our techniques are based on semidefinite programming methods for spherical codes introduced by Bachoc and Vallentin (2008). As a corollary to our bound, we show the nonexistence of spherical tight designs of harmonic index 4 on a sphere in Rn with n≥ 3.

原文	???core.languages.en_GB???
頁（從 - 到）	96-103
頁數	8
期刊	European Journal of Combinatorics
卷	53
DOIs	https://doi.org/10.1016/j.ejc.2015.11.003
出版狀態	已出版 - 1 4月 2016

存取文件

10.1016/j.ejc.2015.11.003

引用此

@article{416d488c91224815ba44c227a9e0899b,

title = "A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4",

abstract = "We give a new upper bound for the cardinality of a set of equiangular lines in Rn with a fixed common angle θ for each (n, θ) satisfying certain conditions. Our techniques are based on semidefinite programming methods for spherical codes introduced by Bachoc and Vallentin (2008). As a corollary to our bound, we show the nonexistence of spherical tight designs of harmonic index 4 on a sphere in Rn with n≥ 3.",

author = "Takayuki Okuda and Yu, {Wei Hsuan}",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Ltd.",

year = "2016",

month = apr,

day = "1",

doi = "10.1016/j.ejc.2015.11.003",

language = "???core.languages.en_GB???",

volume = "53",

pages = "96--103",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

}

TY - JOUR

T1 - A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4

AU - Okuda, Takayuki

AU - Yu, Wei Hsuan

PY - 2016/4/1

Y1 - 2016/4/1

N2 - We give a new upper bound for the cardinality of a set of equiangular lines in Rn with a fixed common angle θ for each (n, θ) satisfying certain conditions. Our techniques are based on semidefinite programming methods for spherical codes introduced by Bachoc and Vallentin (2008). As a corollary to our bound, we show the nonexistence of spherical tight designs of harmonic index 4 on a sphere in Rn with n≥ 3.

AB - We give a new upper bound for the cardinality of a set of equiangular lines in Rn with a fixed common angle θ for each (n, θ) satisfying certain conditions. Our techniques are based on semidefinite programming methods for spherical codes introduced by Bachoc and Vallentin (2008). As a corollary to our bound, we show the nonexistence of spherical tight designs of harmonic index 4 on a sphere in Rn with n≥ 3.

UR - http://www.scopus.com/inward/record.url?scp=84949032770&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2015.11.003

DO - 10.1016/j.ejc.2015.11.003

M3 - 期刊論文

AN - SCOPUS:84949032770

SN - 0195-6698

VL - 53

SP - 96

EP - 103

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

ER -

A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4

摘要

存取文件

指紋

引用此