Construction of storage codes of rate approaching one on triangle-free graphs

Consider an assignment of bits to the vertices of a connected graph Γ ( V , E ) with the property that the value of each vertex is a function of the values of its neighbors. A collection of such assignments is called a storage code of length | V | on Γ . In this paper we construct an infinite family...

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Veröffentlicht in:	Designs, codes, and cryptography codes, and cryptography, 2023-12, Vol.91 (12), p.3901-3913
Hauptverfasser:	Huang, Hexiang, Xiang, Qing
Format:	Artikel
Sprache:	eng
Schlagworte:	Apexes Coding and Information Theory Computer Science Cryptology Discrete Mathematics in Computer Science Graph theory Graphs
Online-Zugang:	Volltext
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Zusammenfassung:	Consider an assignment of bits to the vertices of a connected graph Γ ( V , E ) with the property that the value of each vertex is a function of the values of its neighbors. A collection of such assignments is called a storage code of length \| V \| on Γ . In this paper we construct an infinite family of linear storage codes on triangle-free graphs with rates arbitrarily close to one.
ISSN:	0925-1022 1573-7586
DOI:	10.1007/s10623-023-01278-6