  For a high-rate case, it is difficult to randomly construct good low-density
parity-check (LDPC) codes of short and moderate lengths because their Tanner
graphs are prone to making short cycles. Also, the existing high-rate
quasi-cyclic (QC) LDPC codes can be constructed only for very restricted code
parameters. In this paper, a new construction method of high-rate regular QC
LDPC codes with parity-check matrices consisting of a single row of circulants
with the column-weight 3 or 4 is proposed based on special classes of cyclic
difference families. The proposed QC LDPC codes can be constructed for various
code rates and lengths including the minimum achievable length for a given
design rate, which cannot be achieved by the existing high-rate QC LDPC codes.
It is observed that the parity-check matrices of the proposed QC LDPC codes
have full rank. It is shown that the error correcting performance of the
proposed QC LDPC codes of short and moderate lengths is almost the same as that
of the existing ones through numerical analysis.
