research
∙
08/30/2023
On the difficulty to beat the first linear programming bound for binary codes
The first linear programming bound of McEliece, Rodemich, Rumsey, and We...
share
research
∙
06/10/2022
On some properties of random and pseudorandom codes
We describe some pseudorandom properties of binary linear codes achievin...
research
∙
05/04/2022
Weight distribution of random linear codes and Krawchouk polynomials
For 0 < λ < 1 and n →∞ pick uniformly at random λ n vectors in {0,1}^n a...
research
∙
12/16/2021
Hypercontractive inequalities for the second norm of highly concentrated functions, and Mrs. Gerber's-type inequalities for the second Renyi entropy
Let T_ϵ, 0 ≤ϵ≤ 1/2, be the noise operator acting on functions on the boo...
research
∙
04/29/2021
One more proof of the first linear programming bound for binary codes and two conjectures
We give one more proof of the first linear programming bound for binary ...
research
∙
10/06/2020
An improved bound on ℓ_q norms of noisy functions
Let T_ϵ, 0 ≤ϵ≤ 1/2, be the noise operator acting on functions on the boo...
research
∙
08/17/2020
On codes decoding a constant fraction of errors on the BSC
Using techniques and results from Kudekar et al. we strengthen the bound...
research
∙
09/26/2019
A moment ratio bound for polynomials and some extremal properties of Krawchouk polynomials and Hamming spheres
Let p > 2. We improve the bound f_p/f_2< (p-1)^s/2 for a polynomial f of...
research
∙
07/25/2019
On the Round Complexity of Randomized Byzantine Agreement
We prove lower bounds on the round complexity of randomized Byzantine ag...
research
∙
09/25/2018
