A system and a method for determining a quasi-cyclic (QC) low-density parity-check (LDPC) code, such that the QC LDPC code has no trapping sets are disclosed. A set of matrices representing a family of QC LDPC codes are acquired, wherein each QC LDPC code is a tail-biting spatially-coupled code of girth not less than eight, and wherein each column of each matrix in the set has a weight not less than four. Based on a trapping set pattern, a matrix from the set of matrices is selected such that the matrix represents the QC LDPC code with no trapping sets. The matrix can be stored into a memory.