The Berlekamp-Massey Algorithm. A Sight from Theory of Pade Approximants and Orthogonal Polynomials

In this paper we interpret the Berlekamp-Massey algorithm (BMA) for synthesis of linear feedback shift register (LFSR) as an algorithm computing Pade approximants for Laurent series over arbitrary field. This interpretation of the BMA is based on a iterated procedure for computing of the sequence of polynomials orthogonal to some sequence of polynomial spaces with scalar product depending on the given Laurent series. It is shown that the BMA is equivalent to the Euclidean algorithm of a conversion of Laurent series in continued fractions.