Disclosed are techniques for generating a parity check matrix representing an error correcting code (ECC) for protecting a plurality of bits of a message. In an aspect, a method includes initializing a matrix M to store selected three-bit codes, selecting a first three-bit code from a set L of three-bit combinations of a number of bits n of the ECC that minimizes a sum of squared row weights of each row of the matrix M, comparing the first three-bit code with each of a plurality of error syndromes, and calculating, based on no comparison of the first three-bit code with each of the plurality of error syndromes, new error syndromes and storing the new error syndromes, wherein the new error syndromes are calculated by comparing the first three-bit code with each three-bit code in the matrix M, and storing the first three-bit code in the matrix M.