DFT calculation for the {2}-inverse of a polynomial matrix with prescribed image and kernel

In this paper, we first give the finite algorithm for generalized inverse AT,S(2) of a matrix A over an integral domain, and, based on it and the discrete Fourier transform, present an algorithm for calculating {2}-inverses of a polynomial matrix with prescribed image and kernel. And the algorithm is implemented in the Mathematica programming language and expands the algorithms in [13].