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Families of Fibonacci codes and Fibonacci representations are defined. Their main attributes are robustness, manifesting itself by the local containment of errors; and simple encoding and decoding. The main application explored is the transmission of binary strings in which the length is in an unknown range, using robust Fibonacci representations instead of the conventional error-sensitive logarithmic ramp representation. Though the former is asymptotically longer than the latter, the former is actually shorter for very large initial segments of integers.