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

Mathematics

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

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 (US)
Article number	102513
Journal	Finite Fields and their Applications
Volume	100
DOIs	https://doi.org/10.1016/j.ffa.2024.102513
State	Published - Dec 2024

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

Keywords

Erasure codes
Hypercube
List decodable codes
Turán problems

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10.1016/j.ffa.2024.102513

Cite this

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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",

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

language = "English (US)",

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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.

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KW - Hypercube

KW - List decodable codes

KW - Turán problems

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DO - 10.1016/j.ffa.2024.102513

M3 - Article

AN - SCOPUS:85205339633

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JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

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ER -

Erasure list-decodable codes and Turán hypercube problems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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