Erasure list-decodable codes and Turán hypercube problems

Noga Alon

doi:10.1016/j.ffa.2024.102513

Erasure list-decodable codes and Turán hypercube problems

Noga Alon

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We observe that several vertex Turán 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 Turán density of certain hypergraph augmentations we obtain improved bounds for some of these problems.

Original language	English
Article number	102513
Journal	Finite Fields and their Applications
Volume	100
DOIs	https://doi.org/10.1016/j.ffa.2024.102513
State	Published - 1 Dec 2024
Externally published	Yes

Keywords

Erasure codes
Hypercube
List decodable codes
Turán problems

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

Access to Document

10.1016/j.ffa.2024.102513

Cite this

@article{0fe6faff3745483982b4389d8e8cae93,

title = "Erasure list-decodable codes and Tur{\'a}n hypercube problems",

abstract = "We observe that several vertex Tur{\'a}n 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{\'a}n density of certain hypergraph augmentations we obtain improved bounds for some of these problems.",

keywords = "Erasure codes, Hypercube, List decodable codes, Tur{\'a}n problems",

author = "Noga Alon",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2024",

month = dec,

day = "1",

doi = "10.1016/j.ffa.2024.102513",

language = "English",

volume = "100",

journal = "Finite Fields and their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Erasure list-decodable codes and Turán hypercube problems

AU - Alon, Noga

PY - 2024/12/1

Y1 - 2024/12/1

N2 - We observe that several vertex Turán 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 Turán density of certain hypergraph augmentations we obtain improved bounds for some of these problems.

AB - We observe that several vertex Turán 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 Turán density of certain hypergraph augmentations we obtain improved bounds for some of these problems.

KW - Erasure codes

KW - Hypercube

KW - List decodable codes

KW - Turán problems

UR - https://www.scopus.com/pages/publications/85205339633

U2 - 10.1016/j.ffa.2024.102513

DO - 10.1016/j.ffa.2024.102513

M3 - Article

AN - SCOPUS:85205339633

SN - 1071-5797

VL - 100

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

M1 - 102513

ER -

Erasure list-decodable codes and Turán hypercube problems

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this