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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...
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06/10/2022
On some properties of random and pseudorandom codes
We describe some pseudorandom properties of binary linear codes achievin...
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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...
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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...
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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 ...
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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...
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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...
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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...
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07/25/2019
On the Round Complexity of Randomized Byzantine Agreement
We prove lower bounds on the round complexity of randomized Byzantine ag...
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09/25/2018