A new coding algorithm for trees

We construct a one-to-one mapping between binary vectors of length $n$ and preorder codewords of regular, ordered, oriented, rooted, binary trees having $N \approx n + 2$ log $n$ nodes. The mappings in both directions can be organized in such a way that complexities of all transformations are measured by linear functions of $n$. The approach is then completely extended to non-regular binary trees and partially extended to $D$-ary trees with $D > 2$.