A family of low density parity check (LDPC) codes is generated based on a mother code having a highest code rate. The low density parity check (LDPC) codes include a codeword size of at least 1344. The LDPC codes also include a plurality of parity bits in a lower triangular form. The mother code is constructed by: selecting m number of rows and n number of columns; setting maximum column weights and row weights; designing a protograph matrix based on the set column weights and row weights and selected m and n; and selecting circulant blocks based on the protograph matrix.