  We propose a new low-density parity-check code construction scheme based on
2-lifts. The proposed codes have an advantage of admitting efficient hardware
implementations. With the motivation of designing codes with low error floors,
we present an analysis of the low-weight stopping set distributions of the
proposed codes. Based on this analysis, we propose design criteria for
designing codes with low error floors. Numerical results show that the
resulting codes have low error probabilities over binary erasure channels.
