In this paper, two new families of patterned matrices, i.e., the RSFPrLR circulant matrix and the RSLPrFL circulant matrix in codes over the complex field are considered, respectively. An algorithm for finding the inverse and the group inverse of the RSFPrLR circulant matrix is presented by Euclid algorithm. Extension is made to compute the inverse of the RSLPrFL circulant matrix by using the relationship between an RSFPrLR circulant matrix and an RSLPrFL circulant matrix. Numerical examples are presented to demonstrate the implementation of the proposed algorithm.

RSFPrLR circulant matrix, inverse, group inverse.