Papers for

error-correcting code developers

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

New lattices achieve extremely high kissing numbers in prime dimensions

A lattice family with kissing constant $τ(\mathcal{L}_n) \ge e^{\sqrt{n}}$

Abstract: For prime dimensions $n \ge 5$, we define integer lattices $\mathcal{L}_n$ with kissing constant \begin{align} τ(\mathcal{L}_n) \ge \left(\frac{1}{\sqrt{2 πe}} + o(1)\right) n^{3/4} e^{\sqrt n}. \notag \end{align} This improves on the growth rate $e^{Θ((\log n)^2)}$ of the Barnes-Wall lattices, which provided the previously best known asymptotic lower bound. The construction is an extension of a previous construction by Bennett-Peikert based on Reed-Solomon codes.

Fri 11 SeptInformation Theory
The gist
The paper finds a way to create special grids of points in spaces whose dimension is a prime number greater or equal to five. These grids have a surprisingly large number of spheres that can touch a central sphere without overlapping, much more than previous known constructions. The authors improve on earlier methods by extending a construction that used ideas from error-correcting codes. This means they found denser ways to pack spheres in high-dimensional spaces for certain dimensions.
Open → 2609.13608v1