1. A method of encoding and exporting a plurality of information bits, comprising: (a) providing a parity-check matrix that is equivalent to a modular code matrix that consists of a diagonal sub-matrix structure, including a plurality of diagonal structure sub-matrices, immediately above a connection layer that includes a plurality of contiguous diverse connection layer sub-matrices that have the same number of rows, with all but at most one of the connection layer sub-matrices being below corresponding diagonal structure sub-matrices; (b) using the information bits and the parity-check matrix to compute, via an encoder, a plurality of parity bits; (c) assembling, via the encoder, the information bits and the parity bits to form a codeword; and (d) exporting at least a portion of the codeword to a medium.