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

2023/01/04 by Huang, Hexiang, Xiang, Qing · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.01668

Abstract

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 binary linear storage codes on triangle-free graphs with rates arbitrarily close to one.

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