Bounds on equiangular lines and on related spherical codes

Abstract

An $L$-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set $L$. We show, for a fixed $\alpha ,\beta >0$, that the size of any $[-1,-\beta ]\cup \{\alpha \}$-spherical code is at most linear in the dimension. In particular, this bound applies to sets of lines such that every two are at a fixed angle to each another.

7 pages, final version