A method for operating a memory includes: receiving a first write command and a first write address; receiving first write data a portion of which is masked; reading first read data and a first read error correction code from a region selected based on the first write address in a cell array; detecting and correcting an error in the first read data based on the first read error correction code to produce error-corrected first read data; generating first new write data by replacing the masked portion of the first write data with a portion of the error-corrected first read data; generating a first write error correction code based on the first new write data; and writing the first new write data and the first write error correction code into the region selected based on the first write address in response to the detecting of the error.