An apparatus, method, and an optical storage medium to generate an error correction block include a data block generation unit processing digital data on a byte-by-byte basis and arranging the processed digital data from 0.sup.th to (N-1).sup.th columns and from 0.sup.th to (M-1).sup.th rows to form (M.times.N) data blocks. A matrix block generation unit arranges the (M.times.N) data blocks in K rows according to a data transmission sequence to form a matrix block. A first codeword generation unit adds a first error correction check word of 2.times.K bytes to each of N columns to form a first codeword of ((K.times.M)+2.times.K) bytes. A second codeword generation unit adds a second error correction check word of P bytes to each of ((K.times.M)+2.times.K) rows to form a second codeword of (N+P) bytes.