Bounds for the sum of distances of spherical sets of small size

DOI10.1016/J.DISC.2023.113346zbMATH Open1521.94135arXiv2105.03511MaRDI QIDQ6367128

M. M. Stoyanova, P. G. Boyvalenkov, Alexander Barg

Publication date: 7 May 2021

Abstract: We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $Nsim{n}^{a}lpha,0<alphale2.$ 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.

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Association schemes, strongly regular graphs (05E30) Bounds on codes (94B65) General harmonic expansions, frames (42C15)

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