Spherical Codes from Craig’s Lattices

Spherical codes are collections of points on a high-dimensional sphere with the property that any two points are far apart. They are a classical model for transmitting data reliably over noisy channels. A central goal is to construct codes that are both large and efficiently decodable.

A 2015 result by Bacher implies that Craig's lattices give rise to spherical codes of at least super-polynomial size. In this talk, we show that these codes can also be efficiently (list) decoded. Furthermore, we provide computational evidence that the code size asymptotically outperforms all previously known constructions.