Two-dimensional multiplicative arrays over Zq−1 and girth-6 q-ary QC-LDPC codes based on quadratic-residues modulo p < q

Construction of q-ary quasi-cyclic low-density parity-check (QC-LDPC) codes based on two-dimensional multiplicative arrays over Zq−1, q = 2m, is studied. In particular, two-dimensional arrays formed by the set of quadratic-residue numbers modulo prime numbers less than q are considered.