Erasure codes and Tur\'an hypercube problems
Combinatorics
2024-03-26 v1
Abstract
We observe that several vertex Tur\'an type problems for the hypercube that received a considerable amount of attention in the combinatorial community are equivalent to questions about erasure list-decodable codes. Analyzing a recent construction of Ellis, Ivan and Leader, and determining the Tur\'an density of certain hypergraph augemntations we obtain improved bounds for some of these problems.
Cite
@article{arxiv.2403.16319,
title = {Erasure codes and Tur\'an hypercube problems},
author = {Noga Alon},
journal= {arXiv preprint arXiv:2403.16319},
year = {2024}
}