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