Question: Suppose that a parity check code has minimum distance d. Define the distance between a code word and a received string (of the same length) as the number of bit positions in which the two are different. Show that if the distance between one code word and a given string is less than d/2, the distance between any other code word and the given string must exceed d/2. Show that if a decoder maps a given received string into a code word at smallest distance from the string, all combinations of fewer than d/2 errors will be corrected.