Let S be the set of all binary sequences of length n and Hamming weight at most p. We present  an efficient method to encode elements of S into binary sequences of length O(log |S|). Our encoding/decoding algorithms are faster than the most efficient implementation of enumerative encoding for the same problem, at the expenses of a slight loss in the compression performance. Our method is based on a recently introduced combinatorial structure  that generalizes the classical superimposed codes by Kautz and Singleton, and it allows to perform 
encoding and decoding with  O(nplog (n/p)) bits operations.

We will also discuss the implications of our findings to the efficient transmission of binary sequences over the noiseless OR channel.