  In the paper we are studying some properties of subsets Q of sums of
dissociated sets. The exact upper bound for the number of solutions of the
following equation
  (1) q_1 + ... + q_p = q_{p+1} + ... + q_{2p}, q_i \in Q
  in groups F_2^n is found. Using our approach, we easily prove a recent result
of J. Bourgain on sets of large exponential sums and obtain a tiny improvement
of his theorem. Besides an inverse problem is considered in the article. Let Q
be a set belonging a sumset of two dissociated sets such that equation (1) has
many solutions. We prove that in the case the large proportion of Q is highly
structured.
