A method, computer-readable medium storing instructions, and apparatus for decoding column codewords of a two-dimensional product code having intersecting row and column codewords is presented that reduces the number of computations needed to decode a column codeword. The method includes computing an error location polynomial for all column codewords based on known failure locations in intersecting row codewords, computing a syndrome polynomial for each column codeword, and correcting errors in the column codeword according to error evaluation values generated based on the syndrome polynomial and the stored error location polynomial.