(Code lengthening) A code can be lengthened by one bit by adjoining a parity bit. If this is done, what happens to d and to the error-correcting and error-detecting properties of the code? 8. (Even-weight codes) An even-weight binary code of length n consists of all possible words of length n that have even weight (that is, have an even number of 1's).
(a) How many codewords are there in an even-weight code of length n?
(b) The dual of a code C whose words are of length n is the code C⊥ consisting of all words of length n orthogonal to C. (A word w is in C⊥ if and only if 
for all code words c in C, where here w · c is defined as n i=1 wici. mod 2.) Find C⊥ for the even-weight code C of length n.