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

TL;DR

This paper constructs an infinite family of binary linear storage codes on triangle-free graphs with rates approaching one, advancing the design of efficient storage schemes in graph-based systems.

Contribution

It introduces a novel method for constructing high-rate binary linear storage codes on triangle-free graphs, approaching optimal storage efficiency.

Findings

Constructed an infinite family of codes with rates arbitrarily close to one

Codes are binary linear and defined on triangle-free graphs

Achieved high storage efficiency in graph-based coding schemes

Abstract

Consider an assignment of bits to the vertices of a connected graph $\Gamma(V, E)$ 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 $\Gamma$. In this paper we construct an infinite family of binary linear storage codes on triangle-free graphs with rates arbitrarily close to one.