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diff --git a/v0.3.x/.doctrees/api/galois.BCH.decode.doctree b/v0.3.x/.doctrees/api/galois.BCH.decode.doctree
diff --git a/v0.3.x/.doctrees/api/galois.BCH.detect.doctree b/v0.3.x/.doctrees/api/galois.BCH.detect.doctree
diff --git a/v0.3.x/.doctrees/api/galois.BCH.doctree b/v0.3.x/.doctrees/api/galois.BCH.doctree
diff --git a/v0.3.x/.doctrees/api/galois.BCH.encode.doctree b/v0.3.x/.doctrees/api/galois.BCH.encode.doctree
diff --git a/v0.3.x/.doctrees/api/galois.FieldArray.Random.doctree b/v0.3.x/.doctrees/api/galois.FieldArray.Random.doctree
diff --git a/v0.3.x/.doctrees/api/galois.FieldArray.characteristic_poly.doctree b/v0.3.x/.doctrees/api/galois.FieldArray.characteristic_poly.doctree
diff --git a/v0.3.x/.doctrees/api/galois.FieldArray.column_space.doctree b/v0.3.x/.doctrees/api/galois.FieldArray.column_space.doctree
diff --git a/v0.3.x/.doctrees/api/galois.FieldArray.left_null_space.doctree b/v0.3.x/.doctrees/api/galois.FieldArray.left_null_space.doctree
diff --git a/v0.3.x/.doctrees/api/galois.FieldArray.log.doctree b/v0.3.x/.doctrees/api/galois.FieldArray.log.doctree
diff --git a/v0.3.x/.doctrees/api/galois.FieldArray.minimal_poly.doctree b/v0.3.x/.doctrees/api/galois.FieldArray.minimal_poly.doctree
diff --git a/v0.3.x/.doctrees/api/galois.FieldArray.null_space.doctree b/v0.3.x/.doctrees/api/galois.FieldArray.null_space.doctree
diff --git a/v0.3.x/.doctrees/api/galois.FieldArray.row_space.doctree b/v0.3.x/.doctrees/api/galois.FieldArray.row_space.doctree
diff --git a/v0.3.x/.doctrees/api/galois.Poly.Random.doctree b/v0.3.x/.doctrees/api/galois.Poly.Random.doctree
diff --git a/v0.3.x/.doctrees/api/galois.Poly.derivative.doctree b/v0.3.x/.doctrees/api/galois.Poly.derivative.doctree
diff --git a/v0.3.x/.doctrees/api/galois.Poly.field.doctree b/v0.3.x/.doctrees/api/galois.Poly.field.doctree
diff --git a/v0.3.x/.doctrees/api/galois.Poly.is_irreducible.doctree b/v0.3.x/.doctrees/api/galois.Poly.is_irreducible.doctree
diff --git a/v0.3.x/.doctrees/api/galois.ReedSolomon.decode.doctree b/v0.3.x/.doctrees/api/galois.ReedSolomon.decode.doctree
diff --git a/v0.3.x/.doctrees/api/galois.ReedSolomon.detect.doctree b/v0.3.x/.doctrees/api/galois.ReedSolomon.detect.doctree
diff --git a/v0.3.x/.doctrees/api/galois.ReedSolomon.doctree b/v0.3.x/.doctrees/api/galois.ReedSolomon.doctree
diff --git a/v0.3.x/.doctrees/api/galois.ReedSolomon.encode.doctree b/v0.3.x/.doctrees/api/galois.ReedSolomon.encode.doctree
diff --git a/v0.3.x/.doctrees/api/galois.crt.doctree b/v0.3.x/.doctrees/api/galois.crt.doctree
diff --git a/v0.3.x/.doctrees/api/galois.fermat_primality_test.doctree b/v0.3.x/.doctrees/api/galois.fermat_primality_test.doctree
diff --git a/v0.3.x/.doctrees/api/galois.irreducible_poly.doctree b/v0.3.x/.doctrees/api/galois.irreducible_poly.doctree
diff --git a/v0.3.x/.doctrees/api/galois.irreducible_polys.doctree b/v0.3.x/.doctrees/api/galois.irreducible_polys.doctree
diff --git a/v0.3.x/.doctrees/api/galois.lagrange_poly.doctree b/v0.3.x/.doctrees/api/galois.lagrange_poly.doctree
diff --git a/v0.3.x/.doctrees/api/galois.primitive_element.doctree b/v0.3.x/.doctrees/api/galois.primitive_element.doctree
diff --git a/v0.3.x/.doctrees/api/galois.primitive_poly.doctree b/v0.3.x/.doctrees/api/galois.primitive_poly.doctree
diff --git a/v0.3.x/.doctrees/api/galois.primitive_polys.doctree b/v0.3.x/.doctrees/api/galois.primitive_polys.doctree
diff --git a/v0.3.x/.doctrees/api/galois.primitive_root.doctree b/v0.3.x/.doctrees/api/galois.primitive_root.doctree
diff --git a/v0.3.x/.doctrees/api/galois.primitive_roots.doctree b/v0.3.x/.doctrees/api/galois.primitive_roots.doctree
diff --git a/v0.3.x/.doctrees/api/galois.prod.doctree b/v0.3.x/.doctrees/api/galois.prod.doctree
diff --git a/v0.3.x/.doctrees/api/galois.typing.ShapeLike.doctree b/v0.3.x/.doctrees/api/galois.typing.ShapeLike.doctree
diff --git a/v0.3.x/.doctrees/basic-usage/array-creation.doctree b/v0.3.x/.doctrees/basic-usage/array-creation.doctree
diff --git a/v0.3.x/.doctrees/basic-usage/element-representation.doctree b/v0.3.x/.doctrees/basic-usage/element-representation.doctree
diff --git a/v0.3.x/.doctrees/basic-usage/poly.doctree b/v0.3.x/.doctrees/basic-usage/poly.doctree
diff --git a/v0.3.x/.doctrees/environment.pickle b/v0.3.x/.doctrees/environment.pickle
diff --git a/v0.3.x/.doctrees/getting-started.doctree b/v0.3.x/.doctrees/getting-started.doctree
diff --git a/v0.3.x/api/galois.BCH.decode/index.html b/v0.3.x/api/galois.BCH.decode/index.html
diff --git a/v0.3.x/api/galois.BCH.detect/index.html b/v0.3.x/api/galois.BCH.detect/index.html
@@ -7828,10 +7828,10 @@
 <span class="gp">In [2]: </span><span class="n">GF</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">field</span>
 
 <span class="gp">In [3]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">GF</span><span class="o">.</span><span class="n">Random</span><span class="p">(</span><span class="n">bch</span><span class="o">.</span><span class="n">k</span><span class="p">);</span> <span class="n">m</span>
-<span class="gh">Out[3]: </span><span class="go">GF([1, 0, 1, 0, 0, 1, 0], order=2)</span>
+<span class="gh">Out[3]: </span><span class="go">GF([0, 1, 0, 1, 0, 1, 1], order=2)</span>
 
 <span class="gp">In [4]: </span><span class="n">c</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">);</span> <span class="n">c</span>
-<span class="gh">Out[4]: </span><span class="go">GF([1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1], order=2)</span>
+<span class="gh">Out[4]: </span><span class="go">GF([0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1], order=2)</span>
 </code></pre></div>
 </div>
 <p>Detect no errors in the valid codeword.</p>
@@ -7844,7 +7844,7 @@
 <span class="gh">Out[6]: </span><span class="go">5</span>
 
 <span class="gp">In [7]: </span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">bch</span><span class="o">.</span><span class="n">d</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">^=</span> <span class="mi">1</span><span class="p">;</span> <span class="n">c</span>
-<span class="gh">Out[7]: </span><span class="go">GF([0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1], order=2)</span>
+<span class="gh">Out[7]: </span><span class="go">GF([1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1], order=2)</span>
 
 <span class="gp">In [8]: </span><span class="n">bch</span><span class="o">.</span><span class="n">detect</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
 <span class="gh">Out[8]: </span><span class="go">True</span>
@@ -7858,10 +7858,10 @@
 <span class="gp">In [10]: </span><span class="n">GF</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">field</span>
 
 <span class="gp">In [11]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">GF</span><span class="o">.</span><span class="n">Random</span><span class="p">(</span><span class="n">bch</span><span class="o">.</span><span class="n">k</span> <span class="o">-</span> <span class="mi">3</span><span class="p">);</span> <span class="n">m</span>
-<span class="gh">Out[11]: </span><span class="go">GF([1, 1, 0, 1], order=2)</span>
+<span class="gh">Out[11]: </span><span class="go">GF([1, 1, 1, 1], order=2)</span>
 
 <span class="gp">In [12]: </span><span class="n">c</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">);</span> <span class="n">c</span>
-<span class="gh">Out[12]: </span><span class="go">GF([1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0], order=2)</span>
+<span class="gh">Out[12]: </span><span class="go">GF([1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1], order=2)</span>
 </code></pre></div>
 </div>
 <p>Detect no errors in the valid codeword.</p>
@@ -7874,7 +7874,7 @@
 <span class="gh">Out[14]: </span><span class="go">5</span>
 
 <span class="gp">In [15]: </span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">bch</span><span class="o">.</span><span class="n">d</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">^=</span> <span class="mi">1</span><span class="p">;</span> <span class="n">c</span>
-<span class="gh">Out[15]: </span><span class="go">GF([0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0], order=2)</span>
+<span class="gh">Out[15]: </span><span class="go">GF([0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1], order=2)</span>
 
 <span class="gp">In [16]: </span><span class="n">bch</span><span class="o">.</span><span class="n">detect</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
 <span class="gh">Out[16]: </span><span class="go">True</span>
@@ -7889,15 +7889,15 @@
 
 <span class="gp">In [19]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">GF</span><span class="o">.</span><span class="n">Random</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="n">bch</span><span class="o">.</span><span class="n">k</span><span class="p">));</span> <span class="n">m</span>
 <span class="gh">Out[19]: </span>
-<span class="go">GF([[0, 0, 1, 1, 1, 0, 1],</span>
-<span class="go">    [0, 1, 0, 0, 0, 1, 0],</span>
-<span class="go">    [0, 1, 0, 0, 1, 0, 0]], order=2)</span>
+<span class="go">GF([[0, 1, 1, 0, 0, 1, 1],</span>
+<span class="go">    [1, 1, 0, 1, 1, 0, 0],</span>
+<span class="go">    [1, 0, 1, 0, 1, 0, 1]], order=2)</span>
 
 <span class="gp">In [20]: </span><span class="n">c</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">);</span> <span class="n">c</span>
 <span class="gh">Out[20]: </span>
-<span class="go">GF([[0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0],</span>
-<span class="go">    [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1],</span>
-<span class="go">    [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]], order=2)</span>
+<span class="go">GF([[0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0],</span>
+<span class="go">    [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1],</span>
+<span class="go">    [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]], order=2)</span>
 </code></pre></div>
 </div>
 <p>Detect no errors in the valid codewords.</p>
@@ -7917,9 +7917,9 @@
 
 <span class="gp">In [26]: </span><span class="n">c</span>
 <span class="gh">Out[26]: </span>
-<span class="go">GF([[1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0],</span>
-<span class="go">    [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1],</span>
-<span class="go">    [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]], order=2)</span>
+<span class="go">GF([[1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0],</span>
+<span class="go">    [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1],</span>
+<span class="go">    [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]], order=2)</span>
 
 <span class="gp">In [27]: </span><span class="n">bch</span><span class="o">.</span><span class="n">detect</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
 <span class="gh">Out[27]: </span><span class="go">array([ True,  True,  True])</span>
@@ -7934,15 +7934,15 @@
 
 <span class="gp">In [30]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">GF</span><span class="o">.</span><span class="n">Random</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="n">bch</span><span class="o">.</span><span class="n">k</span> <span class="o">-</span> <span class="mi">3</span><span class="p">));</span> <span class="n">m</span>
 <span class="gh">Out[30]: </span>
-<span class="go">GF([[0, 1, 1, 0],</span>
-<span class="go">    [1, 0, 1, 0],</span>
-<span class="go">    [0, 0, 1, 0]], order=2)</span>
+<span class="go">GF([[1, 1, 0, 0],</span>
+<span class="go">    [0, 1, 0, 0],</span>
+<span class="go">    [1, 0, 1, 1]], order=2)</span>
 
 <span class="gp">In [31]: </span><span class="n">c</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">);</span> <span class="n">c</span>
 <span class="gh">Out[31]: </span>
-<span class="go">GF([[0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1],</span>
-<span class="go">    [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0],</span>
-<span class="go">    [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]], order=2)</span>
+<span class="go">GF([[1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1],</span>
+<span class="go">    [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0],</span>
+<span class="go">    [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]], order=2)</span>
 </code></pre></div>
 </div>
 <p>Detect no errors in the valid codewords.</p>
@@ -7962,9 +7962,9 @@
 
 <span class="gp">In [37]: </span><span class="n">c</span>
 <span class="gh">Out[37]: </span>
-<span class="go">GF([[1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1],</span>
-<span class="go">    [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0],</span>
-<span class="go">    [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]], order=2)</span>
+<span class="go">GF([[0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1],</span>
+<span class="go">    [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0],</span>
+<span class="go">    [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]], order=2)</span>
 
 <span class="gp">In [38]: </span><span class="n">bch</span><span class="o">.</span><span class="n">detect</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
 <span class="gh">Out[38]: </span><span class="go">array([ True,  True,  True])</span>

diff --git a/v0.3.x/api/galois.BCH.encode/index.html b/v0.3.x/api/galois.BCH.encode/index.html
@@ -7885,15 +7885,15 @@
 <span class="gp">In [2]: </span><span class="n">GF</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">field</span>
 
 <span class="gp">In [3]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">GF</span><span class="o">.</span><span class="n">Random</span><span class="p">(</span><span class="n">bch</span><span class="o">.</span><span class="n">k</span><span class="p">);</span> <span class="n">m</span>
-<span class="gh">Out[3]: </span><span class="go">GF([0, 0, 0, 0, 1, 1, 0], order=2)</span>
+<span class="gh">Out[3]: </span><span class="go">GF([0, 0, 0, 0, 1, 0, 0], order=2)</span>
 
 <span class="gp">In [4]: </span><span class="n">c</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">);</span> <span class="n">c</span>
-<span class="gh">Out[4]: </span><span class="go">GF([0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1], order=2)</span>
+<span class="gh">Out[4]: </span><span class="go">GF([0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0], order=2)</span>
 </code></pre></div>
 </div>
 <p>Compute the parity symbols only.</p>
 <div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><code><span class="gp">In [5]: </span><span class="n">p</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">output</span><span class="o">=</span><span class="s2">&quot;parity&quot;</span><span class="p">);</span> <span class="n">p</span>
-<span class="gh">Out[5]: </span><span class="go">GF([1, 0, 0, 1, 0, 1, 0, 1], order=2)</span>
+<span class="gh">Out[5]: </span><span class="go">GF([1, 1, 1, 0, 0, 1, 1, 0], order=2)</span>
 </code></pre></div>
 </div>
 </div>
@@ -7904,15 +7904,15 @@
 <span class="gp">In [7]: </span><span class="n">GF</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">field</span>
 
 <span class="gp">In [8]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">GF</span><span class="o">.</span><span class="n">Random</span><span class="p">(</span><span class="n">bch</span><span class="o">.</span><span class="n">k</span> <span class="o">-</span> <span class="mi">3</span><span class="p">);</span> <span class="n">m</span>
-<span class="gh">Out[8]: </span><span class="go">GF([0, 0, 0, 0], order=2)</span>
+<span class="gh">Out[8]: </span><span class="go">GF([1, 0, 1, 1], order=2)</span>
 
 <span class="gp">In [9]: </span><span class="n">c</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">);</span> <span class="n">c</span>
-<span class="gh">Out[9]: </span><span class="go">GF([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], order=2)</span>
+<span class="gh">Out[9]: </span><span class="go">GF([1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1], order=2)</span>
 </code></pre></div>
 </div>
 <p>Compute the parity symbols only.</p>
 <div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><code><span class="gp">In [10]: </span><span class="n">p</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">output</span><span class="o">=</span><span class="s2">&quot;parity&quot;</span><span class="p">);</span> <span class="n">p</span>
-<span class="gh">Out[10]: </span><span class="go">GF([0, 0, 0, 0, 0, 0, 0, 0], order=2)</span>
+<span class="gh">Out[10]: </span><span class="go">GF([1, 0, 1, 1, 1, 1, 1, 1], order=2)</span>
 </code></pre></div>
 </div>
 </div>
@@ -7924,23 +7924,23 @@
 
 <span class="gp">In [13]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">GF</span><span class="o">.</span><span class="n">Random</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="n">bch</span><span class="o">.</span><span class="n">k</span><span class="p">));</span> <span class="n">m</span>
 <span class="gh">Out[13]: </span>
-<span class="go">GF([[0, 0, 0, 0, 1, 0, 0],</span>
-<span class="go">    [1, 1, 1, 1, 0, 1, 0],</span>
-<span class="go">    [1, 1, 0, 1, 0, 0, 0]], order=2)</span>
+<span class="go">GF([[1, 1, 0, 1, 1, 0, 0],</span>
+<span class="go">    [1, 1, 0, 0, 1, 0, 0],</span>
+<span class="go">    [0, 0, 1, 1, 0, 1, 1]], order=2)</span>
 
 <span class="gp">In [14]: </span><span class="n">c</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">);</span> <span class="n">c</span>
 <span class="gh">Out[14]: </span>
-<span class="go">GF([[0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0],</span>
-<span class="go">    [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0],</span>
-<span class="go">    [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]], order=2)</span>
+<span class="go">GF([[1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1],</span>
+<span class="go">    [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0],</span>
+<span class="go">    [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]], order=2)</span>
 </code></pre></div>
 </div>
 <p>Compute the parity symbols only.</p>
 <div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><code><span class="gp">In [15]: </span><span class="n">p</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">output</span><span class="o">=</span><span class="s2">&quot;parity&quot;</span><span class="p">);</span> <span class="n">p</span>
 <span class="gh">Out[15]: </span>
-<span class="go">GF([[1, 1, 1, 0, 0, 1, 1, 0],</span>
-<span class="go">    [1, 1, 0, 0, 1, 0, 0, 0],</span>
-<span class="go">    [1, 0, 0, 0, 0, 0, 0, 1]], order=2)</span>
+<span class="go">GF([[0, 1, 1, 0, 0, 1, 1, 1],</span>
+<span class="go">    [0, 1, 1, 1, 1, 0, 1, 0],</span>
+<span class="go">    [1, 0, 0, 0, 0, 1, 0, 1]], order=2)</span>
 </code></pre></div>
 </div>
 </div>
@@ -7952,23 +7952,23 @@
 
 <span class="gp">In [18]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">GF</span><span class="o">.</span><span class="n">Random</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="n">bch</span><span class="o">.</span><span class="n">k</span> <span class="o">-</span> <span class="mi">3</span><span class="p">));</span> <span class="n">m</span>
 <span class="gh">Out[18]: </span>
-<span class="go">GF([[0, 0, 1, 0],</span>
-<span class="go">    [1, 0, 1, 1],</span>
-<span class="go">    [0, 1, 1, 0]], order=2)</span>
+<span class="go">GF([[1, 0, 0, 0],</span>
+<span class="go">    [1, 0, 0, 0],</span>
+<span class="go">    [0, 1, 0, 1]], order=2)</span>
 
 <span class="gp">In [19]: </span><span class="n">c</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">);</span> <span class="n">c</span>
 <span class="gh">Out[19]: </span>
-<span class="go">GF([[0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1],</span>
-<span class="go">    [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1],</span>
-<span class="go">    [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]], order=2)</span>
+<span class="go">GF([[1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1],</span>
+<span class="go">    [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1],</span>
+<span class="go">    [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]], order=2)</span>
 </code></pre></div>
 </div>
 <p>Compute the parity symbols only.</p>
 <div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><code><span class="gp">In [20]: </span><span class="n">p</span> <span class="o">=</span> <span class="n">bch</span><span class="o">.</span><span class="n">encode</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">output</span><span class="o">=</span><span class="s2">&quot;parity&quot;</span><span class="p">);</span> <span class="n">p</span>
 <span class="gh">Out[20]: </span>
-<span class="go">GF([[0, 1, 1, 1, 0, 0, 1, 1],</span>
-<span class="go">    [1, 0, 1, 1, 1, 1, 1, 1],</span>
-<span class="go">    [1, 0, 0, 1, 0, 1, 0, 1]], order=2)</span>
+<span class="go">GF([[0, 0, 0, 1, 1, 1, 0, 1],</span>
+<span class="go">    [0, 0, 0, 1, 1, 1, 0, 1],</span>
+<span class="go">    [0, 0, 1, 1, 0, 1, 1, 1]], order=2)</span>
 </code></pre></div>
 </div>
 </div>