(3) Consider the parity check error correcting code on words of length n (i.e. f : B" - But1 is the code that attaches a parity digit 0 or 1 to length n words depending on whether the word has even or odd number of 1s). Show that the image of this code (i.e. the codewords) are precisely those words in But which has even number of Is. Find the matrix for this code. For partial marks, do this for n = 3. 2 (Hint: For the generator matrix, think about how the parity digit can be written as a sum of the digits in the original word. Keep in mind that we are working modulo 2.)