A method of generating an error correction circuit for correcting an error in a codeword read from a memory includes: constructing a generation matrix; transforming the generating matrix into a systematic form, wherein the transformed generating matrix is composed of a parity matrix and a check matrix; sorting rows of the parity matrix according to row weights; determining a number of rows in the parity matrix to be truncated; generating a truncated parity matrix by keeping the sorted rows of the P matrix that have weights less than or equal to weights of the truncated rows of the P matrix so as to minimize a number of logic gate operations; and forming an error correction circuit with the number of logic gate operations minimized according to the truncated P matrix to correct the error of the codeword.