24 citations · 79 across the 31 of their papers we have counts for
10 papers · 1 filter
Energy bounds for weighted spherical codes and designs via linear programming
Sergiy Borodachov, Peter Boyvalenkov, Peter Dragnev +3
Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar -- every attaining code is…
Universal minima of discrete potentials for sharp spherical codes
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
This article is devoted to the study of discrete potentials on the sphere in for sharp codes. We show that the potentials of most of the known sharp codes attain the…
Log-optimal (d+2)-configurations in d-dimensions
Peter D. Dragnev, Oleg R. Musin
We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attai…
Upper bounds for energies of spherical codes of given cardinality and separation
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
We introduce a linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance. Using Hermite interpol…
Universal bounds for spherical codes: the Levenshtein framework lifted
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
Based on the Delsarte-Yudin linear programming approach, we extend Levenshtein's framework to obtain lower bounds for the minimum -energy of spherical codes of prescribed dimens…
Energy Bounds for Codes in Polynomial Metric Spaces
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
In this article we present a unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces). The lower bound…
On spherical codes with inner products in a prescribed interval
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval of . An intricate rela…
Energy bounds for codes and designs in Hamming spaces
Peter G. Boyvalenkov, Peter D. Dragnev, Douglas P. Hardin +2
We obtain universal bounds on the energy of codes and for designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow unified treatment, and can be v…
Universal upper and lower bounds on energy of spherical designs
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are vali…
Universal lower bounds for potential energy of spherical codes
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
We derive and investigate lower bounds for the potential energy of finite spherical point sets (spherical codes). Our bounds are optimal in the following sense -- they cannot be im…