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The variable size list decoder (VLD) was first discussed by Forney (1968), which selects more than one candidate message if the message passes the given criterion. Though the list decoder is seldom used for applications, it is well-known that the generalized Viterbi algorithm (GVA) employs the fixed size list decoder (FLD) in its mean process. In this paper, we propose the GVA which uses VLD, instead of FLD. Then the coding theorem is obtained.