A method for operating a memory includes: reading data and an error correction code from a memory core; correcting an error of the read data based on the read error correction code to produce error-corrected data; generating new data by replacing a portion of the error-corrected data with write data, the portion becoming a write data portion; generating a new error correction code based on the new data; and writing the write data portion of the new data and the new error correction code into the memory core.