A notes on trees and codes

We propose a code based on weighted trees and on the difficulty to reconstruct the weights of the tree from the distances D_{i,j} among the leaves; precisely we consider an ordered rooted tree as code key; we put the letters of the message, translated into numbers, on the edges of the tree as their weights, by starting from the edges coming out from the root, then the edges coming out from the vertices of intrinsic distance 1 from the root and so on. Then we forecast the numbers D_{i,j} for i,j leaves of the tree.