It is shown that the generalized Berlekamp-Massey algorithm (GBMA, in short) for solving the linear synthesis problem of a multi-sequence r over F 2 can be obtained naturally from a special form of the multi-continued fraction algorithm, called the multi-strict continued fraction algorithm (m-SCFA, in short). Moreover, the discrepancy sequence in acting GBMA on r is expressed explicitly by the data associated to the multi-strict continued fraction expansion C( r ) which is obtained by applying m-SCFA on r . As a consequence, a 1-1 correspondence between multi-sequences of any given length and certain multi-strict continued fractions is established.