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.

存储代码是对连通图G ( V , E ) 顶点的符号分配，其属性是每个顶点的值是其邻居值的函数，或者更一般地说，是该图的某个邻域值的函数。 G中的顶点。在这项工作中，我们引入了一种新的存储代码构造方法，使人们能够通过由可解析设计驱动的交错过程从已知代码构造新代码。我们还研究了\({\mathbb Z}\)和\({\mathbb Z}^2\) （线和网格）上的存储代码，找到了几个一维和二维系统容量的封闭式表达式，具体取决于在他们的恢复集上，使用存储代码、图、反码和避免差异集之间的连接。