Two generalizations of ideal matrices and their applications

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.