.. _sphx_glr_api_gallery_communications_coding:

Coding
------

Single-error-correcting block codes.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Frustrated by weekend computer runs aborted by a single bad relay, Richard Hamming (1950) designed codes that correct errors rather than merely detect them. In the (7,4) code three parity bits sit at positions 1, 2 and 4. When one bit flips, the failing parity checks, read as a binary number, give its position (~engineeringkit.communications.hamming74_encode, hamming74_decode). Any two codewords differ in at least three places (~engineeringkit.communications.hamming_distance), which is what makes single-error correction possible.">

.. only:: html

  .. image:: /api/gallery/communications/coding/images/thumb/sphx_glr_plot_01_hamming_code_thumb.png
    :alt:

  :doc:`/api/gallery/communications/coding/plot_01_hamming_code`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hamming's single-error-correcting code</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/communications/coding/plot_01_hamming_code