Let A = {a, b, c, d, e, f, g, h, i}. There are 9 4 = 126 possible 4 element subsets of A. We can encode these subsets with fixed density binary strings of length 9 with exactly 4 ones. Define the following encoding scheme. Given F, a 4-element subset of A, construct a 9-bit string with a 1 in position x if x is in F and with a 0 in position x if x is not in F. For example, the subset {a, c, h, i} corresponds to the binary string: 101000011.