Document Type

Presentation

Presentation Date

Summer 8-20-2015

Conference Name

10th Summer School in Potential Theory

Conference Location

Budapest, Hungary

Peer Review

Invited

Abstract

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

Keywords

Energy bounds, maximal spherical codes, universal configurations

Disciplines

Analysis | Discrete Mathematics and Combinatorics

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