  In this paper, we show that Quasi-Cyclic LDPC codes can efficiently
accommodate the hybrid iterative/ML decoding over the binary erasure channel.
We demonstrate that the quasi-cyclic structure of the parity-check matrix can
be advantageously used in order to significantly reduce the complexity of the
ML decoding. This is achieved by a simple row/column permutation that
transforms a QC matrix into a pseudo-band form. Based on this approach, we
propose a class of QC-LDPC codes with almost ideal error correction performance
under the ML decoding, while the required number of row/symbol operations
scales as $k\sqrt{k}$, where $k$ is the number of source symbols.
