k-Point semidefinite programming bounds for equiangular lines

被引：4
作者：
de Laat, David [1 ]
Machado, Fabricio Caluza [2 ]
de Oliveira Filho, Fernando Mario [1 ]
Vallentin, Frank [3 ]
机构：
[1] Delft Univ Technol, Delft Inst Appl Math, Mekelweg 4, NL-2628 CD Delft, Netherlands
[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil
[3] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany
来源：
MATHEMATICAL PROGRAMMING | 2022年 / 194卷 / 1-2期
基金：
巴西圣保罗研究基金会;
关键词：
52C17; 90C22; SETS;
D O I：
10.1007/s10107-021-01638-x
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We propose a hierarchy of k-point bounds extending the Delsarte-Goethals-Seidel linear programming 2-point bound and the Bachoc-Vallentin semidefinite programming 3-point bound for spherical codes. An optimized implementation of this hierarchy allows us to compute 4, 5, and 6-point bounds for the maximum number of equiangular lines in Euclidean space with a fixed common angle.
引用
收藏
页码：533 / 567
页数：35
相关论文
共 47 条
  • [1] [Anonymous], 1971, PhD thesis
  • [2] New upper bounds for kissing numbers from semidefinite programming
    Bachoc, Christine
    Vallentin, Frank
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 21 (03) : 909 - 924
  • [3] Lower Bounds for Measurable Chromatic Numbers
    Bachoc, Christine
    Nebe, Gabriele
    de Oliveira Filho, Fernando Mario
    Vallentin, Frank
    [J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2009, 19 (03) : 645 - 661
  • [4] Bannai Ei., 2004, ALGEBR ANAL, P1, DOI DOI 10.1090/S1061-0022-05-00868-X
  • [5] New bounds for equiangular lines
    Barg, Alexander
    Yu, Wei-Hsuan
    [J]. DISCRETE GEOMETRY AND ALGEBRAIC COMBINATORICS, 2014, 625 : 111 - 121
  • [6] New Bounds for Spherical Two-Distance Sets
    Barg, Alexander
    Yu, Wei-Hsuan
    [J]. EXPERIMENTAL MATHEMATICS, 2013, 22 (02) : 187 - 194
  • [7] Barvinok A., 2002, A course in convexity
  • [8] Julia: A Fresh Approach to Numerical Computing
    Bezanson, Jeff
    Edelman, Alan
    Karpinski, Stefan
    Shah, Viral B.
    [J]. SIAM REVIEW, 2017, 59 (01) : 65 - 98
  • [9] BOUNDS ON EQUIANGULAR LINES AND ON RELATED SPHERICAL CODES
    Bukh, Boris
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2016, 30 (01) : 549 - 554
  • [10] Universally optimal distribution of points on spheres
    Cohn, Henry
    Kumar, Abhinav
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 20 (01) : 99 - 148
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