The matrix G = [I_4 | A], where G = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 | 0 1 1 1 0 1 1 1 0 1 1 1] is a generator matrix in standard form for a [7, 4] that we denote by H_3, By Theorem binary code 1.2.1 a parity check matrix for H_3 is H = ['A^T | I_3] = [0 1 1 1 1 0 1 1 1 1 0 1 | 1 0 0 0 1 0 0 0 1] This code is called the [7, 4] Hamming code. Find at least four information sets in the [7, 4] code H_3 from Example 1.2.3. Find at least one set of four coordinates that do not form an information set. Often in this text we will refer to a subcode of a code c. If c is not linear (or not known to be linear), a subcode of C is any subset of c. If c is linear, a subcode will be a subset of C which must also be linear; in this case a subcode of c is a subspace of c