Synthesizing all linearized shift-registers of the minimal or required length
Vladimir R. Sidorenko, Martin Bossert · 2010
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 IF qm is considered. This algorithm, which is a generalization of the Berlekamp-Massey algorithm, has time complexity (N 2 ) 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 .