Provided is a systematic encoder of cyclic codes for partially written codewords in flash memories wherein all bits of an erased but unwritten area have a default value such as one. In the case where the host writes data to one or a plurality of discontinuous fragments in an area reserved for storing the message section of a codeword in the flash memory, the encoder computes the parity of the codeword by using only the data written to the flash memory as input and by asserting that all bits in the gaps between the written fragments have the default erased value, such that after both the data and the parity are written to the flash memory, the area reserved for storing the codeword would contain a valid codeword. On read back, the host reads the entire codeword area from the flash memory without having to distinguish between the written and unwritten fragments.