Hamming code: Difference between revisions

Revision as of 19:08, 10 January 2022

Revision as of 19:09, 10 January 2022

Line 171:

Algorithms. John Wiley and Sons, 2005.(Cap. 3) {{ISBN|978-0-471-64800-0}}</ref>

Since [7, &nbsp;4, &nbsp;3] = &nbsp;[''n'', &nbsp;''k'', &nbsp;''d''] = &nbsp;[2^''m'' &nbsp;− &nbsp;1, 2^''m''−1−&nbsp;−&nbsp;1&nbsp;−&nbsp;''m'', &nbsp;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''&nbsp;−&nbsp;''k'')-[[identity matrix]].