Upper bounds for energies of spherical codes of given cardinality and separation

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 interpolation we construct polynomials to derive corresponding bounds. These bounds are universal in the sense that they are val...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2020-09, Vol.88 (9), p.1811-1826
Main Authors: Boyvalenkov, P. G., Dragnev, P. D., Hardin, D. P., Saff, E. B., Stoyanova, M. M.
Format: Article
Language:English
Subjects:
Codes
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Hermite polynomials
Interpolation
Linear programming
Mathematical analysis
Potential energy
Special Issue: Coding and Cryptography 2019
Upper bounds
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Summary: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 interpolation we construct polynomials to derive corresponding bounds. These bounds are universal in the sense that they are valid for all absolutely monotone potential functions and the required interpolation nodes do not depend on the potentials.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-020-00733-y