Bounds for the sum of distances of spherical sets of small size
Bounds for the sum of distances of spherical sets of small size
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DOI：
10.1016/j.disc.2023.113346
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
A. Barg;P. Boyvalenkov;Maya M. Stoyanova
中科院分区：
文献类型：
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作者：
A. Barg;P. Boyvalenkov;Maya M. Stoyanova
当N= Θ（n α），0< α 2时，我们推导出n维尺寸为N的球形码距离之和的上界和下界。的界限是由专门最近的一般，普遍的能量范围的球面集。我们讨论了我们的界限的渐近行为沿着与几个例子的代码的距离之和密切遵循的上限。
We derive upper and lower bounds on the sum of distances of a spherical code of size N in n dimensions when N= Θ (n α), 0< α⩽ 2. The bounds are derived by specializing recent general, universal bounds on energy of spherical sets. We discuss asymptotic behavior of our bounds along with several examples of codes whose sum of distances closely follows the upper bound.