Noah Stephens-Davidowitz

activity

20182026

collaborators

3 papers

math.MG2026

Lattices with Large Kissing Number from Local Density

Huck Bennett, Minki Hhan, Zihan Li +1

Let $κ_{p} (n)$ denote the maximum kissing number of a lattice $L \subset R^{n}$ . We prove that $κ_{p} (n) \geq 2^{Ω (n)}$ for all $p \geq 1$ and that $κ_p(n) \geq Ω…

cs.DS2024

More basis reduction for linear codes: backward reduction, BKZ, slide reduction, and more

Surendra Ghentiyala, Noah Stephens-Davidowitz

We expand on recent exciting work of Debris-Alazard, Ducas, and van Woerden [Transactions on Information Theory, 2022], which introduced the notion of basis reduction for codes, in…

math.MG2018

Kissing numbers and transference theorems from generalized tail bounds

Stephen D. Miller, Noah Stephens-Davidowitz

We generalize Banaszczyk's seminal tail bound for the Gaussian mass of a lattice to a wide class of test functions. From this we obtain quite general transference bounds, as well a…