A memory system includes a memory controller including: a memory core configured to store data and an error correction code corresponding to the data; a syndrome generator configured to generate a first syndrome by substituting the data and the error correction code, read from the memory core, into a first check matrix, and generate a second syndrome by substituting the data and the error correction code, read from the memory core, into a second check matrix; and an error correction unit configured to correct an error of the read data and error correction code by using the first syndrome and the second syndrome, wherein constituents having values of ‘1’ in the first check matrix have values of ‘1’ also in the second check matrix.