@Article{GR95,
  author = 	 { David Gillman and Ronald L. Rivest },
  title = 	 { Complete Variable-Length ``Fix-Free'' Codes },
  journal = 	 { Designs, Codes and Cryptography },
  publisher =    { Springer },                  
  issn =         { 0925-1022 },
  OPTyear = 	 { 1995 },
  date =         { 1995 },                  
  volume = 	 { 5 },
  number = 	 { 2 },
  OPTkey = 	 {},
  pages = 	 { 109--114 },
  url =          { http://dx.doi.org/10.1007/BF01397665 },
  doi =          { 10.1007/BF01397665 },
  abstract =     {
        A set of codewords is \emph{fix-free} if it is both prefix-free and suffix-free: no codeword in the set
        is a prefix or a suffix of any other. A set of codewords $\{ x_1 , x_2 , \ldots, x_n \}$ over 
        a $t$-letter alphabet $\Sigma$ is said to be \emph{complete} if it satisfies the Kraft
        inequality with equality, so that 
        \[ 
           \sum_{1\leq i \leq n} {t^{ - \left| {x_i } \right|} } = 1.
        \]
        The set $\Sigma^k$ of all codes of length $k$ is obviously both free-free and complete.
        We show, surprisingly, that there are other examples of complete fix-free codes, ones whose
        codewords have a variety of lengths.  We discuss such variable-length (complete) fix-free
        codes and techniques for constructing them.                  
                  },
}