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Since [7, 4, 3] = [''n'', ''k'', ''d''] = [2<sup>''m''</sup> − 1, 2<sup>''m''</sup> − 1 − ''m'', 3]. The [[parity-check matrix]] '''H''' of a Hamming code is constructed by listing all columns of length ''m'' that are pair-wise independent.
Thus '''H''' is a matrix whose left side is all of the nonzero ''n''-tuples where order of the ''n''-tuples in the columns of matrix does not matter. The right hand side is just the (''n'' − ''k'')-[[identity matrix]].
So '''G''' can be obtained from '''H''' by taking the transpose of the left hand side of '''H''' with the identity ''k''-[[identity matrix]] on the left hand side of '''G'''.
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