10th Summer School in Potential Theory
In this work in progress report we shall present the framework to extend the universal lower energy bounds to subclasses of codes with with distinct inner products on a subinterval $[\ell,1]$, where $-1< \ell < 1$. The essential ingredient is orthogonality with respect to positive definite signed measures up to degree $k$, that is signed measures $\nu$ for which $\int p^2 (t)d\nu(t) >0$ for all polynomials $p(t)$ of degree at most $k$. In particular, we shall obtain a Levenshtein-type bounds on cardinality of codes with distinct inner products in $[\ell,s]$ for suitable $-1<\ell
Energy bounds, maximal spherical codes, universal configurations
Analysis | Discrete Mathematics and Combinatorics
Peter D. Dragnev, Peter Boyvalenkov, Douglas P. Hardin, Edward Saff, and Maya Stoyanova (2015).
Levenshtein-type bounds for codes with inner products in prescribed interval. Presented at 10th Summer School in Potential Theory, Budapest, Hungary.