1. Construct a list of all complementary codes of block length 4. How many pairs are there on the list? Show that essentially there is only one pair. We say that two code word pairs are essentially the same if one can be turned into the other by the operations of replacing either code word by its negative or of replacing either code word by its reciprocal.
2. The two components of a real complementary code are used as the in-phase and quadrature components of an MSK pulse. Prove that all sidelobes in the matched-filter output for this MSK pulse are in phase quadrature to the main lobe.