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A storage code is an assignment of symbols to the vertices of a connectedgraph $G(V,E)$ with the property that the value of each vertex is a function ofthe values of its neighbors, or more generally, of a certain neighborhood ofthe vertex in $G$. In this work we introduce a new construction method ofstorage codes, enabling one to construct new codes from known ones via aninterleaving procedure driven by resolvable designs. We also study storagecodes on $\mathbb Z$ and ${\mathbb Z}^2$ (lines and grids), finding closed-formexpressions for the capacity of several one and two-dimensional systemsdepending on their recovery set, using connections between storage codes,graphs, anticodes, and difference-avoiding sets.

Storage codes and recoverable systems on lines and grids