  An algorithm for constructing parity-check matrices of non-binary
quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The
algorithm finds short cycles in the base matrix and tries to eliminate them by
selecting the circulants and the elements of GF(q). Firstly the algorithm tries
to eliminate the cycles with the smallest number edges going outside the cycle.
The efficiency of the algorithm is demonstrated by means of simulations. In
particular, it was shown that NB QC-LDPC codes constructed with use of our
algorithm loose less that 0.1 dB in comparison to the best NB LDPC codes.
