Refined Convergents to the Associated Continued Fractions for Binary Sequences

作     者：Dai Zongduo Zeng Kencheng State Key Laboratory of Information Security Academia Sinica Beijing, 100039 China 

作者机构：State Key Laboratory of Information Security Academia Sinica Beijing China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1994年第10卷第2期

页      面：179-191页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Refined Convergents to the Associated Continued Fractions for Binary Sequences 

摘      要：The relation between continued fractions and Berlekamp’s algorithm was studied by some 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 can be interpreted in terms of continued fractions. In this paper, we first introduce the so-called refined convergents to the continued fraction expansion of a binary sequence s, and then give a thorough answer to the question in the context of Massey’s linear feedback shift register synthesis algorithm 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.