  Fibonacci codes are self-synchronizing variable-length codes that are proven
useful for their robustness and compression capability. Asymptotically, these
codes provide better compression efficiency as the order of the underlying
Fibonacci sequence increases, but at the price of the increased suffix length.
We propose a circumvention to this problem by introducing higher-dimensional
Fibonacci codes for integer vectors. In the process, we provide extensive
theoretical background and generalize the theorem of Zeckendorf to higher
order. As thus, our work unify several variations of Zeckendorf's theorem while
also providing new grounds for its legitimacy.
