The noiseless wire-tap channel of type II with coset coding scheme was provided by Ozarow and Wyner. In this correspondence, the user is split into multiple parties who are coordinated in coding their data symbols by using the same encoder. The adversary can tap not only partial transmitted symbols but also partial data symbols. We are interested in the equivocation of the data symbols to this adversary who has more power than that of Ozarow and Wyner. The generalized Hamming weight of Wei and the dimension/length profile (DLP of Forney are extended to two-code formats: relative generalized lower bounds of the new concepts are investigated. They are useful to design a perfect secrecy coding scheme for the coordinated multiparty model. Under a general secrecy standard, the coordinated model can provide a higher transmission rate than an uncoordinated (time-sharing) model.