Alex Samorodnitsky

activity

20002026

most citedHafnians, perfect matchings and Gaussian matrices

29 citations · 99 across the 31 of their papers we have counts for

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21 papers · 1 filter

math.CO2024

Eigenvalues and eigenfunctions of a Hamming ball

Amit Avni, Alex Samorodnitsky

We describe the eigenvalues and the eigenspaces of the adjacency matrices of subgraphs of the Hamming cube induced by Hamming balls, and more generally, by a union of adjacent conc…

math.CO2022

Weight distribution of random linear codes and Krawchouk polynomials

Alex Samorodnitsky

For $0 < λ < 1$ and $n \to \infty$ pick uniformly at random $λn$ vectors in ${0, 1}^{n}$ and let $C$ be the orthogonal complement of their span. Given $0 < γ < \frac{1}{2}$ with $…

math.CO2019★ 1 cited

A moment ratio bound for polynomials and some extremal properties of Krawchouk polynomials and Hamming spheres

Naomi Kirshner, Alex Samorodnitsky

Let $p \geq 2$ . We improve the bound $\frac{∥ f ∥ _{p}}{∥ f ∥ _{2}} \leq (p - 1)^{s /2}$ for a polynomial $f$ of degree $s$ on the boolean cube ${0, 1}^{n}$ , which comes from hypercontractivit…

math.CO2018

On coset leader graphs of structured linear codes

Eran Iceland, Alex Samorodnitsky

We suggest a new approach to obtain bounds on locally correctable and some locally testable binary linear codes, by arguing that these codes (or their subcodes) have coset leader g…

math.CO2018

On $ℓ_{4} : ℓ_{2}$ ratio of functions with restricted Fourier support

Naomi Kirshner, Alex Samorodnitsky

Given a subset $A \subseteq {0, 1}^{n}$ , let $μ (A)$ be the maximal ratio between $ℓ_{4}$ and $ℓ_{2}$ norms of a function whose Fourier support is a subset of $A$ . We make some sim…

math.CO2014

Bounds on the permanent and some applications

Leonid Gurvits, Alex Samorodnitsky

We give new lower and upper bounds on the permanent of a doubly stochastic matrix. Combined with previous work, this improves on the deterministic approximation factor for the perm…