  A cross-bifix-free code is a set of words in which no prefix of any length of
any word is the suffix of any word in the set. Cross-bifix-free codes arise in
the study of distributed sequences for frame synchronization. We provide a new
construction of cross-bifix-free codes which generalizes the construction in
Bajic (2007) to longer code lengths and to any alphabet size. The codes are
shown to be nearly optimal in size. We also establish new results on Fibonacci
sequences, that are used in estimating the size of the cross-bifix-free codes.
