The relation between continued fractions and Berlekamp’s algorithm was studied bysome reseachers. The latter is an iterative procedure proposed for decoding BCH codes. However,there remains an unanswered question whether each of the iterative steps in the algorithm canbe interpreted in terms of continued fractions. In this paper, we first introduce the so-calledrefined convergents to the continued fraction expansion of a binary sequence s, and then give athorough answer to the question in the context of Massey’s linear feedback shift register synthesisalgorithm which is equivalent to that of Berlekamp, and at last we prove that there exists a one-to-one correspondence between the n-th refined convergents and the length n segments.
