The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. In this paper, we provide some general results on parity-check codes from disjunct matrices. We then examine properties such as rate, distance, girth, and density of the families of codes obtained from three specific constructions of disjunct matrices.

翻译：线性码的矩阵表示作为分离矩阵（disjunct matrices）已被广泛研究。然而，此前尚未建立分离矩阵的性质与其衍生校验矩阵码之间的关联。本文给出了从分离矩阵构造校验矩阵码的通用结果，进而考察了由三种具体分离矩阵构造方法得到的码族在码率、距离、围长及密度等方面的性质。