On Coset Leader Graphs of Structured Linear Codes

Eran Iceland; Alex Samorodnitsky

doi:10.1007/s00454-019-00129-3

On Coset Leader Graphs of Structured Linear Codes

Eran Iceland, Alex Samorodnitsky

Hebrew University of Jerusalem

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

3 Scopus citations

Abstract

We suggest a new approach to obtain bounds on locally correctable and some locally testable binary linear codes, by arguing that these codes (or their subcodes) have coset leader graphs with high discrete Ricci curvature. The bounds we obtain for locally correctable codes are worse than the best known bounds obtained using quantum information theory, but are better than those obtained using other methods, such as the “usual” information theory. (We remark that our methods are completely elementary.) The bounds we obtain for a family of locally testable codes improve the best known bounds.

Original language	English
Pages (from-to)	560-576
Number of pages	17
Journal	Discrete and Computational Geometry
Volume	63
Issue number	3
DOIs	https://doi.org/10.1007/s00454-019-00129-3
State	Published - 1 Apr 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Funding

Funders	Funder number
Israel Science Foundation	1241/11, 1724/15

Keywords

Discrete curvature
Linear codes
Locally correctable codes

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10.1007/s00454-019-00129-3

Cite this

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On Coset Leader Graphs of Structured Linear Codes

Abstract

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Keywords

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