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We design a forest with nodes that represent orthogonal variable spreading factor (OVSF) sequences of different lengths (spreading codes of different lengths that can be used for multi-rate DS-CDMA). In addition to the non-descendant OVSF property exhibited in well-known tree-structured generation of sequences [(F. Adachi, et al., 1997) and (E.H. Dinan and B. Jabbari, 1998)], the sequences represented by the nodes of our forest have useful properties that can be used to achieve multi-channel communication (with a sequence providing a channel) with a lower total peak-to-mean envelope power ratio (PMEPR). These OSVF sequences grouped by our forest structure also have properties that facilitate symbol-by-symbol adaptation of the symbol duration in multi-rate CDMA systems. For example, certain lineages in the forest have the property that any pair of code sequences in the same lineage are shift orthogonal to each other, with the unit shift length being that of the shorter sequence. We present the forest-structured generation of the sequences (spreading codes) and their properties.