I found this in my discrete math lecture notes on error correcting codes, and was immediately confused as this should obviously be wrong. I even found a counterexample: v=101, w=010. Here v-w=011 so wt(v-w)=2, but v+w=0111 so wt(v+w)=3. I'm not sure what could be wrong about this counterexample. I am probably missing something.
This is probably very elementary, but I am scared to discredit something my professor had no problem telling her class whilst studying for a final. And, if this is true, what can be said about this "counterexample"?