Memory system and method for controlling non-volatile memory

A method for controlling a non-volatile memory, the method comprising:

• generating an error correction code based on user data received from a host, the error correction code including a first symbol group and a second symbol group, the first symbol group being a set of symbols shared between a first component code and at least one of a third component code and a fourth component code, the second symbol group being a set of symbols shared between a second component code and at least one of the third component code and the fourth component code;
• and
• storing the error correction code in the non-volatile memory,
• wherein the generation of the error correction code comprises:
• encoding the first component code with a lower correction capability than the second component code;
• encoding the third component code with a lower correction capability than the fourth component code;
• setting a ratio of symbols shared between the second component code and the third component code in the second symbol group to be smaller than a ratio of symbols shared between the first component code and the third component code in the first symbol group;
• and
• setting a ratio of symbols shared between the second component code and the fourth component code in the second symbol group to be larger than a ratio of symbols shared between the first component code and the fourth component code in the first symbol group.