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.

翻译：存储码是将符号分配给连通图$G(V,E)$顶点的一种赋值方式，其性质为每个顶点的值是该顶点邻居（或更一般地，图中该顶点某一特定邻域）值的函数。本文提出了一种新的存储码构造方法，该方法通过由可分解设计驱动的交织过程，从已知码构造新码。我们同时研究了$\mathbb Z$和${\mathbb Z}^2$（线图和网格）上的存储码，利用存储码、图、反码和差分避免集之间的联系，推导出若干一维和二维系统（取决于其恢复集）容量的闭式表达式。