<正>TherelationbetweencontinuedfractionsandBerlekamp’salgorithmwasstudiedbysomereseachers.ThelatterisaniterativeprocedureproposedfordecodingBCHcodes.However,thereremainsanunansweredquestionwhethereachoftheiterativestepsinthealgorithmcanbeinterpretedintermsofcontinuedfractions.Inthispaper,wefirstintroducetheso-calledrefinedconvergentstothecontinuedfractionexpansionofabinarysequences,andthengiveathoroughanswertothequestioninthecontextofMassey’slinearfeedbackshiftregistersynthesisalgorithmwhichisequivalenttothatofBerlekamp,andatlastweprovethatthereexistsaone-to-onecorrespondencebetweenthen-threfinedconvergentsandthelengthnsegments.
