Abstract: A method of transmitting a message includes, for each data block, generating a root matrix using a generator, generating a quasi-cyclic matrix H using the root matrix, encoding the block using H to create a codeword, and transmitting the codeword. The root matrix includes three submatrices: an identity matrix in an upper-left-hand portion of the root matrix, an identity matrix in a lower-left-hand portion of the root matrix, and a circulant matrix in a right-hand portion of the root matrix. The circulant matrix equals the sum of an identity matrix and an identity matrix with rows shifted once to the right. Generating H includes expanding the root matrix by replacing 0 elements in the root matrix by a square matrix of 0 elements and replacing 1 elements in the root matrix by a shifted diagonal matrix. Non-zero elements of the diagonal matrix are selected from GF(q) based on the generator.