Bounds on antipodal spherical designs with few angles
文献类型：期刊论文
| 作者 | Xu, Zhiqiang1,2; Xu, Zili1,2; Yu, Wei-Hsuan3 |
| 刊名 | ELECTRONIC JOURNAL OF COMBINATORICS
 |
| 出版日期 | 2021-08-13 |
| 卷号 | 28期号:3页码:21 |
| ISSN号 | 1077-8926 |
| DOI | 10.37236/9891 |
| 英文摘要 | A finite subset X on the unit sphere S-d is called an s-distance set with strength t if its angle set A(X) := {< x, y > : x, y is an element of X, x not equal y} has size s, and X is a spherical t-design but not a spherical (t + 1)-design. In this paper, we consider to estimate the maximum size of such antipodal set X for small s. Motivated by the method developed by Nozaki and Suda, for each even integer s is an element of [ t+5/2, t + 1] with t >= 3, we improve the best known upper bound of Delsarte, Goethals and Seidel. We next focus on two special cases: s = 3, t = 3 and s = 4, t = 5. Estimating the size of X for these two cases is equivalent to estimating the size of real equiangular tight frames (ETFs) and Levenstein-equality packings, respectively. We improve the previous estimate on the size of real ETFs and Levenstein-equality packings. This in turn gives an upper bound on vertical bar X vertical bar when s = 3, t = 3 and s = 4, t = 5, respectively. |
| 资助项目 | Beijing Natural Science Foundation[Z180002] ; NSFC[12025108] ; NSFC[11688101] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000685640000001 |
| 出版者 | ELECTRONIC JOURNAL OF COMBINATORICS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59113]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Xu, Zhiqiang |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China 3.Natl Cent Univ, Math Dept, Taoyuan, Taiwan |
| 推荐引用方式 GB/T 7714 | Xu, Zhiqiang,Xu, Zili,Yu, Wei-Hsuan. Bounds on antipodal spherical designs with few angles[J]. ELECTRONIC JOURNAL OF COMBINATORICS,2021,28(3):21. |
| APA | Xu, Zhiqiang,Xu, Zili,&Yu, Wei-Hsuan.(2021).Bounds on antipodal spherical designs with few angles.ELECTRONIC JOURNAL OF COMBINATORICS,28(3),21. |
| MLA | Xu, Zhiqiang,et al."Bounds on antipodal spherical designs with few angles".ELECTRONIC JOURNAL OF COMBINATORICS 28.3(2021):21. |
入库方式： OAI收割
来源：数学与系统科学研究院
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