Complete variable-length ``fix-free'' codes (Q1345134)

A set of codewords is said to be fix-free if it is both prefix-free and suffix-free. A set of codewords \(\{x_ 1, x_ 2, \dots, x_ n\}\) over a \(t\)-letter alphabet \(\Sigma\) is said to be complete if it satisfies the equality \(\sum_{1\leq i\leq n} t^{-| x_ i|} =1\) (the Kraft inequality with equality). The authors give a construction of a complete fix-free code that gives a ratio of the longest word to the shortest word approaching 3. They further generalize this by developing a recursive construction which gives arbitrarily large ratios.