A generalization of Gerzon's bound on spherical s-distance sets

TL;DR

This paper extends Gerzon's bound to a broader class of spherical s-distance sets using polynomial methods, providing a new upper limit on their size.

Contribution

It introduces a generalized upper bound for spherical s-distance sets, expanding the scope beyond equiangular sets through polynomial techniques.

Findings

Derived a new upper bound for spherical s-distance sets

Generalizes Gerzon's bound to broader classes of sets

Uses polynomial methods to establish bounds

Abstract

We Use the method of linearly independent polynomials to derive an upper bound for the cardinality of a spherical s-distance set F where the sum of distinct inner products of any two elements from F is zero. Our result generalizes the well-known Gerzon's bound for the cardinality of an equiangular spherical set to a significantly broader class of spherical s-distance sets.