Binary codes of length $n$ may be viewed as subsets of vertices of the Boolean hypercube $\{0,1\}^n$. The ability of a linear error-correcting code to recover erasures is connected to influences of particular monotone Boolean functions. These functions provide insight into the role that particular coordinates play in a code's erasure repair capability. In this paper, we consider directly the influences of coordinates of a code. We describe a family of codes, called codes with minimum disjoint support, for which all influences may be determined. As a consequence, we find influences of repetition codes and certain distinct weight codes. Computing influences is typically circumvented by appealing to the transitivity of the automorphism group of the code. Some of the codes considered here fail to meet the transitivity conditions requires for these standard approaches, yet we can compute them directly.

翻译：长度为 $n$ 的二元码可视为布尔超立方体 $\{0,1\}^n$ 顶点子集。线性纠错码恢复擦除的能力与特定单调布尔函数的影响相关。这些函数揭示了特定坐标在码的擦除修复能力中所起的作用。本文直接研究码的坐标影响。我们描述了一类称为最小不相交支撑码的码族，其所有影响均可确定。由此推导出重复码及某些等重码的影响。通常通过利用码的自同构群的传递性来避免计算影响。本文考虑的某些码不满足这些标准方法所需的传递性条件，但我们仍能直接计算它们。