Error correction code engine of semiconductor memory device and semiconductor memory device

Abstract

An ECC engine of a semiconductor memory device includes an ECC encoder and an ECC decoder. The ECC encoder generates parity data based on main data based on a primitive polynomial and stores a codeword including the main data and the parity data in a target page. The ECC decoder reads the codeword from the target page based on an address to generate a syndrome and corrects at least one error bit in the read codeword based on the syndrome by respectively applying different syndromes to a single bit error in the read codeword, adjacent bit errors and non-adjacent bit errors occurring in non-adjacent two memory cells in the target page. The ECC decoder generates the different syndromes based on a parity check matrix generated as a function of the primitive polynomial. The primitive polynomial has an alpha matrix as a solution belonging to a Galois field.