  In the paper, we define the concept of the quantum hash generator and offer
design, which allows to build a large amount of different quantum hash
functions. The construction is based on composition of classical
$\epsilon$-universal hash family and a given family of functions -- quantum
hash generator.
  The proposed construction combines the properties of robust presentation of
information by classical error-correcting codes together with the possibility
of highly compressed presentation of information by quantum systems.
  In particularly, we present quantum hash function based on Reed-Solomon code,
and we proved, that this construction is optimal in the sense of number of
qubits needed.
