A memory system may include an error correction code generation circuit configured to generate a first error correction code having a large bit number by using write data and a first H matrix in a first error correction mode, and to generate a second error correction code having a small bit number by using the write data and a second H matrix in a second error correction mode, and a memory core configured to store the first error correction code and the write data in the first error correction mode, and to store the second error correction code and the write data in the second error correction mode.