Resolvable 2-designs for regular low-density parity-check codes

This paper extends the class of low-density parity-check (LDPC) codes that can be algebraically constructed. We present regular LDPC codes based on resolvable Steiner 2-designs which have Tanner graphs free of four-cycles. The resulting codes are (3, ρ)-regular or (4, ρ)-regular for any value of ρ and for a flexible choice of code lengths.