  We obtain a bijection between some set of multidimensional sequences and this
of $d$-type plane forests which is based on the breadth first search algorithm.
This coding sequence is related to the sequence of population sizes indexed by
the generations, through a Lamperti type transformation. The same
transformation in then obtained in continuous time for multitype branching
processes with discrete values. We show that any such process can be obtained
from a $d^2$ dimensional compound Poisson process time changed by some integral
functional. Our proof bears on the discretisation of branching forests with
edge lengths.
