English

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}
}
R2 v1 2026-06-28T15:31:58.834Z