NAND multi-level cell (MLC) flash memories are widely used due to low cost and high capacity. However, the increased number of levels in MLC results in larger interference and errors. The errors in MLC flash memories tend to be directional and limited-magnitude. Many related works focus on asymmetric errors, but bidirectional errors also occur because of the bidirectional interference and the adjustment of the hard-decision reference voltages. To take advantage of the characteristics, we propose t bidirectional (l_u,l_d) limited-magnitude error correction codes, which can reduce errors more effectively. The proposed code is systematic, and can correct t bidirectional errors with upward and downward magnitude of l_u and l_d, respectively. The proposed method is advantageous in that the parity size is reduced, and it has lower bit error rate than conventional error correction codes with the same code rate.