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$\{0,1\}^n$顶点集的子集。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联。这些函数揭示了特定坐标在代码擦除修复能力中所起的作用。本文直接考虑代码坐标的影响。我们描述了一类称为最小不相交支撑码的代码族，该类代码的所有影响均可确定。由此，我们得到了重复码和某些特定权重码的影响。通常通过利用代码自同构群的传递性来规避对影响的计算。本文所考虑的某些代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的影响。