1. A method for determining a quasi-cyclic (QC) low-density parity-check (LDPC) code, such that the QC LDPC code has no trapping sets, comprising the steps of: acquiring a set of matrices representing a family of QC LDPC codes, 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; selecting, based on a trapping set pattern, a matrix from the set of matrices, such that the matrix represents the QC LDPC code with no trapping sets, wherein the trapping set pattern is a pattern of six bits in a corresponding Tanner graph; and storing the matrix into a memory, wherein the steps of the method are performed by a processor.