The Norm Spectrum of Barnes-Wall Lattices Below Twice the Minimum

Yuhang Cao, Sihuang Hu, Hexiang Huang +1

Let ${\Lambda }_m$ be the Barnes-Wall lattice of dimension $2^m$, normalized to have minimum squared norm $d_m:=2^{m-1}$. We determine its complete norm spectrum strictly between $d_m$ and…