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0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 1 &amp; 0 &amp; 1 &amp; 0 &amp; 1 \end{pmatrix}. \end{equation} One may check that <span>$\mathrm{rowspace}(\overline{G}(1, 4)) \cong \mathrm{rowspace}(G_X)$</span> and <span>$\mathrm{rowspace}(\overline{G}(2, 4)) \cong$</span>\
<span>$\mathrm{rowspace}(G_Z)$</span> via the permutation <span>$(3 \,\, 5 \,\, 9 \,\, 15 \,\, 13 \,\, 14 \,\, 12 \,\, 7 \,\, 11 \,\, 8 \,\, 4)$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../The Vardy-Be’ery Decomposition/">« The Vardy-Be’ery Decomposition</a><a class="docs-footer-nextpage" href="../../Classical/linear_code/">Linear Codes »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.24 on <span class="colophon-date" title="Wednesday 14 February 2024 19:14">Wednesday 14 February 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<span>$\mathrm{rowspace}(G_Z)$</span> via the permutation <span>$(3 \,\, 5 \,\, 9 \,\, 15 \,\, 13 \,\, 14 \,\, 12 \,\, 7 \,\, 11 \,\, 8 \,\, 4)$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../The Vardy-Be’ery Decomposition/">« The Vardy-Be’ery Decomposition</a><a class="docs-footer-nextpage" href="../../Classical/linear_code/">Linear Codes »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.24 on <span class="colophon-date" title="Friday 1 March 2024 16:27">Friday 1 March 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/Examples/The Vardy-Be’ery Decomposition/index.html
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julia&gt; C_P_full = augment(C_block, generator_matrix(QC));

julia&gt; are_equivalent(C_P_full, C_big_P)
true</code></pre><p>It is also possible to work these theorems backwards by choosing a desired subcode then seeing if a supercode can be built to contain it.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Tutorials/Weight Reduction/">« Weight Reduction</a><a class="docs-footer-nextpage" href="../Quantum Reed-Muller Codes/">Quantum Reed-Muller Codes »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.24 on <span class="colophon-date" title="Wednesday 14 February 2024 19:14">Wednesday 14 February 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
true</code></pre><p>It is also possible to work these theorems backwards by choosing a desired subcode then seeing if a supercode can be built to contain it.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Tutorials/Weight Reduction/">« Weight Reduction</a><a class="docs-footer-nextpage" href="../Quantum Reed-Muller Codes/">Quantum Reed-Muller Codes »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.24 on <span class="colophon-date" title="Friday 1 March 2024 16:27">Friday 1 March 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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