The BCH Family of Storage Codes on Triangle-Free Graphs is of Unit Rate

Haihua Deng, Hexiang Huang, Guobiao Weng +1

Let $\Gamma$ be a simple connected graph on $n$ vertices, and let $C$ be a code of length $n$ whose coordinates are indexed by the vertices of $\Gamma$. We say that $C$ is a \textit{storage…