A simple Hankel interpretation of the Berlekamp-Massey algorithm

Abstract

A simple interpretation of the Berlekamp-Massey algorithm in the light of the Hankel matrix is presented. The salient result is that the jump of the linear feedback shift register (LFSR) length is derived almost trivially from the so-called Iohvidov index of the Hankel matrix, prior to making any reference to the Berlekamp-Massey algorithm itself. Next, the Hankel system of equations that yields the updated connection polynomial is solved via the natural LU factorization of the Hankel matrix, which itself leads to the Berlekamp-Massey algorithm in a simple and transparent manner.