1. Balanced and constant functions as seen by Hadamard 1111 11 11 1 1 1 1 1 1 = 4 0 0 0 Matrix M Vector V Vector S This is number of minterms “0” in the function This is measure of correlation with other rows of M Constant 0 Ones in map encoded by “-1”, zeros by “1”

2. Balanced and constant functions as seen by Hadamard 1111 11 11 1 1 = - 4 0 0 0 Matrix M Vector V Vector S This is number of minterms “1” in the function This is measure of correlation with other rows of M Constant 1

3. Balanced and constant functions as seen by Hadamard 1111 11 11 1 1 1 1 = 0 4 0 0 Matrix M Vector V Vector S balanced This means we have half “1” and half “0s”

4. Local patterns for Affine functions 1010 0101 1010 0101 1100 0011 1100 0011 00 01 11 10 ab cd a  b  c  d  1