  In this survey we concern ourself with the question, wether there exists a
fix-free code for a given sequence of codeword lengths. For a given alphabet,
we obtain the {\em Kraftsum} of a code, if we divide for every length the
number of codewords of this length in the code by the total number of all
possible words of this length and then take summation over all codeword lengths
which appears in the code. The same way the Kraftsum of a lengths sequence
$(l_1,..., l_n) $ is given by $\sum_{i=1}^n q^{-l_i} $, where $q$ is the
numbers of letters in the alphabet. Kraft and McMillan have shown in
\cite{kraft} (1956), that there exists a prefix-free code with codeword lengths
of a certain lengths sequence, if the Kraftsum of the lengths sequence is
smaller than or equal to one. Furthermore they have shown, that the converse
also holds for all (uniquely decipherable) codes.\footnote{In this survey a
code means a set of words, such that any message which is encoded with these
words can be uniquely decoded. Therefore we omit in future the "uniquely
decipherable" and write only "code".} The question rises, if Kraft's and
McMillan's result can be generalized to other types of codes? Throughout, we
try to give an answer on this question for the class of fix-free codes. Since
any code has Kraftsum smaller than or equal to one, this answers the question
for the second implication of Kraft-McMillan's theorem. Therefore we pay
attention mainly to the first implication.
