Storage Codes on Coset Graphs with Asymptotically Unit Rate

A storage code on a graph G is a set of assignments of symbols to the vertices such that every vertex can recover its value by looking at its neighbors. We consider the question of constructing large-size storage codes on triangle-free graphs constructed as coset graphs of binary linear codes. Previously it was shown that there are infinite families of binary storage codes on coset graphs with rate converging to 3/4. Here we show that codes on …