In this letter, we investigate the separating redundancy of binary linear codes. Using analytical techniques, we provide a general lower bound on the first separating redundancy of binary linear codes and show the bound is tight for a particular family of binary linear codes, i.e., cycle codes. In other words, the first separating redundancy of cycle codes can be determined. We also derive a deterministic and constructive upper bound on the second separating redundancy of cycle codes, which is shown to be better than the general deterministic and constructive upper bounds for the codes.

In this letter, we propose an appealing class of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) cycle codes. The parity-check matrix is carefully designed such that the corresponding generator matrix has some nice properties: 1) systematic, 2) quasi-cyclic, and 3) sparse, which allows a parallel encoding with low complexity. Simulation results show that the performance of the proposed encoding-aware LDPC codes is comparable to that of the progressive-edge-growth (PEG) constructed nonbinary LDPC cycle codes.