## Mathematical Sciences Faculty Presentations

Presentation

Summer 8-20-2015

#### Conference Name

10th Summer School in Potential Theory

#### Conference Location

Budapest, Hungary

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

COinS

#### Link to Original Published Item

http://www.renyi.hu/conferences/sspt/presentations.html