Synthesizing all linearized shift-registers of the minimal or required length

An efficient algorithm synthesizing all q-linearized shift-registers of the minimal or required length generating a sequence of length N over a finite field F_qm is considered. This algorithm, which is a generalization of the Berlekamp-Massey algorithm, has time complexity O(N²) operations in IF_qm, and can be applied for efficient solving the key equation when decoding Gabidulin codes up to and beyond half the minimum rank distance .