In this paper, two kinds of generalizations of ideal matrices, generalized ideal matrices and double ideal matrices. are obtained and studied, The concepts of generalized ideal matrices and double ideal matrices are proposed, and their ranks and maxima.linearly independent groups are verified.The initial motivation to study double cyclic matrices is to study the quasi cyclic codes of the fractional index. In this paper, the generalized form of the quasi cyclic codes, i.e. the {\phi}-quasi cyclic codes. and the construction of the generated matrix are given by the double ideal matrix.

翻译：本文获得并研究了理想矩阵的两种推广形式，即广义理想矩阵与双理想矩阵。提出了广义理想矩阵与双理想矩阵的概念，并验证了它们的秩及极大线性无关组。研究双循环矩阵的初始动机源于对分数指标准循环码的探讨。本文通过双理想矩阵给出了准循环码的推广形式，即φ-准循环码，并构造了其生成矩阵。