A method for accessing a memory module includes; encoding first data of a first partial burst length to generate first parities and first cyclic redundancy codes, encoding second data of a second partial burst length to generate second parities and second cyclic redundancy codes, writing the first data and the second data to first memory devices, and writing the first parities, the first cyclic redundancy codes, the second parities, and the second cyclic redundancy codes to a second memory device and a third memory device.