Delsarte-Yudin LP Method and Universal Lower Bounds on Energy
2015 Workshop on Combinatorics and Applications at SJTU
Shanghai Jiao Tong University, Shanghai, China
We derive universal lower bounds for the potential energy of spherical codes and codes in Hamming spaces, that are optimal in the framework of Delsarte's linear programming approach adapted for energy bounds by Yudin. Our bounds are universal in the sense of both Levenshtein and Cohn-Kumar; i.e., they are valid for any choice of dimension and code cardinality and they apply to any absolutely monotone potential.
Spherical codes, potential energy, universally optimal configurations
Analysis | Discrete Mathematics and Combinatorics | Other Applied Mathematics | Other Physical Sciences and Mathematics
Peter D. Dragnev (2015).
Delsarte-Yudin LP Method and Universal Lower Bounds on Energy. Presented at 2015 Workshop on Combinatorics and Applications at SJTU, Shanghai Jiao Tong University, Shanghai, China.