The mechanism named ``Superimposed coding''  allows to
store a set of data of variable size into a bit-string of fixed
size. It is then possible, with a simple test, to estimate the
probability that an element is in the set of data (which depends
on the size of the result bit-string and on the number of data).
This probability is equal to 0 if the output of the test is
More precisely, the result is an -bit string named . We note where each . Initially, is set to . We have then elements of various size and we note the set of data . Moreover, let us define hash functions where each with .
For we compute and for every we put to 1 the bit where .
To know if the element is in the set of data , we compute for every and if there is an element such as then . If not, then with an error probability of about .