The Voronoi Region of the Barnes-Wall Lattice $\Lambda_{16}$
Information Theory
2024-10-28 v1 math.IT
Metric Geometry
Abstract
We give a detailed description of the Voronoi region of the Barnes-Wall lattice , including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.
Keywords
Cite
@article{arxiv.2301.06092,
title = {The Voronoi Region of the Barnes-Wall Lattice $\Lambda_{16}$},
author = {Daniel Pook-Kolb and Erik Agrell and Bruce Allen},
journal= {arXiv preprint arXiv:2301.06092},
year = {2024}
}
Comments
8 pages, 2 figures. This work has been submitted to the IEEE for possible publication