Take, for example, a 15*15 Identity matrix with a row of 15 1's added to the bottom. When multiplied with a (n*15) matrix, this will generate a (n*16) matrix where the number added to the end of each row is the sum of the first 15 bits, in other words, it adds an odd parity bit. (Considering only 1's and 0's with mod 2 arthmitic, BTW) OK, so that 16*15 matrix is the generating matrix that creates the codewords from the original plain data. How do you make the check matrix - a matrix that gives a zero matrix when multiplied with the codeword matrix, eg. after data transmission, to confirm the integrity of the data?