Exercise 3 Find at least four information sets in the [7, 4] code H3 from Example 1.2.3. Find at least one set of four coordinates that do not form an information set. Example 1.2.3 The matrix G = [14A], where si 0 1 0 0 0 0 1 11 0100101 G= 0010110 Lo 0 0 0 11 1 1 is a generator matrix in standard form for a [7, 4] binary code that we denote by H3. By Theorem 1.2.1 a parity check matrix for H3 is o 11111007 0 1 H =[A" | 13] = 1 011010 1 1 0 1 0 0 1 This code is called the [7, 4] Hamming code. 1