29 citations · 99 across the 31 of their papers we have counts for
37 papers
On the OpenAI whole-cube bound
Alex Samorodnitsky
This is an essentially derivative note, whose goal is to interpret the 'whole-cube' bound of OpenAI for binary codes in a possibly somewhat more accessible way. This is attained, i…
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…
Optimal Discrimination Between Two Pure States and Dolinar-Type Coherent-State Detection
Itamar Katz, Alex Samorodnitsky, Yuval Kochman
We consider the problem of discrimination between two pure quantum states. It is well known that the optimal measurement under both the error-probability and log-loss criteria is a…
On the difficulty to beat the first linear programming bound for binary codes
Alex Samorodnitsky
The first linear programming bound of McEliece, Rodemich, Rumsey, and Welch is the best known asymptotic upper bound for binary codes, for a certain subrange of distances. Starting…
On some properties of random and pseudorandom codes
Alex Samorodnitsky
We describe some pseudorandom properties of binary linear codes achieving capacity on the binary erasure channel under bit-MAP decoding (as shown in Kudekar et al this includes dou…
Weight distribution of random linear codes and Krawchouk polynomials
Alex Samorodnitsky
For and pick uniformly at random vectors in and let be the orthogonal complement of their span. Given with $…