The Nonsingularity of FLS r-Circulant Matrices

Since the good properties and structure of the FLS r-circulant matrices, they have wide application, such as in the generalized cyclic codes. In this paper, motivated by [1], we give some discriminations by using only the elements in the first row of the FLS r-circulant matrix on non singularity, give an example at last and show the feasibility of these methods by the example.