Polynomial-time construction of spherical codes

Abstract

We give a simple lower bound for the dimensions of the families of polynomially constructible spherical codes of given minimal angle φ, deduced from the analog of the Katsman-Tsfasman-Vlăduţ bound for linear codes. In particular the supremum τpol of the numbers log2 CardX/dim X, where X ranges over all polynomially constructible families of spherical codes with φ ≥ π/3, is such that τpol ≥ 2/15.