Given a real dataset and a computation family, we wish to encode and store the dataset in a distributed system so that any computation from the family can be performed by accessing a small number of nodes. In this work, we focus on the families of linear computations where the coefficients are restricted to a finite set of real values. For two-valued computations, a recent work presented a scheme that gives good feasible points on the access-redundancy tradeoff. This scheme is based on binary covering codes having a certain closure property. In a follow-up work, this scheme was extended to all finite coefficient sets, using a new additive-combinatorics notion called coefficient complexity. In the present paper, we explore non-binary covering codes and develop schemes that outperform the state-of-the-art for some coefficient sets. We provide a more general coefficient complexity definition and show its applicability to the access-redundancy tradeoff.

翻译：给定一个真实数据集和一个计算族，我们希望将数据集编码并存储于分布式系统中，使得该计算族中的任意计算都能通过访问少量节点完成。本文聚焦于系数限于有限实数值集合的线性计算族。针对二值计算，近期研究提出了一种方案，在访问-冗余权衡中给出了良好的可行点。该方案基于具有特定封闭性质的二进制覆盖码。在后续研究中，该方案通过一种名为系数复杂度的新型加性组合学概念，被推广至所有有限系数集合。本文探索了非二进制覆盖码，并开发出针对某些系数集合优于现有技术的方案。我们提出了更广义的系数复杂度定义，并展示了其在访问-冗余权衡中的适用性。