Bounds on equiangular lines and on related spherical codes

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 $α,β>0$, that the size of any $[-1,-β]\cup\{α\}$-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.

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