<p><a href="https://en.wikipedia.org/wiki/Multiplication_table" class="extiw" title="w:Multiplication table">Multiplication table</a> of <a href="https://en.wikipedia.org/wiki/Nimber" class="extiw" title="w:Nimber">Nimbers</a>; compare <span style="white-space:nowrap"><a href="https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="Sloane's"><img alt="Sloane's" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/11px-OEISicon_light.svg.png" decoding="async" width="11" height="15" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/17px-OEISicon_light.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/22px-OEISicon_light.svg.png 2x" data-file-width="409" data-file-height="556"></a> <a href="//oeis.org/A051775" class="extiw" title="oeis:A051775">A051775</a></span>, <span style="white-space:nowrap"><a href="https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="Sloane's"><img alt="Sloane's" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/11px-OEISicon_light.svg.png" decoding="async" width="11" height="15" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/17px-OEISicon_light.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/22px-OEISicon_light.svg.png 2x" data-file-width="409" data-file-height="556"></a> <a href="//oeis.org/A051910" class="extiw" title="oeis:A051910">A051910</a></span>
</p><p>The nonzero elements form the <a href="https://en.wikipedia.org/wiki/Cayley_table" class="extiw" title="w:Cayley table">Cayley table</a> of <a href="https://en.wikipedia.org/wiki/List_of_small_groups#List_of_small_abelian_groups" class="extiw" title="w:List of small groups">Z<sub>15</sub></a>, as shown below.
</p><p>Below the <a href="https://en.wikiversity.org/wiki/User:Watchduck/hat#Dual_matrix" class="extiw" title="v:User:Watchduck/hat">dual matrix</a>, showing permuted binary <a href="https://en.wikipedia.org/wiki/Walsh_matrix" class="extiw" title="w:Walsh matrix">Walsh matrices</a>.<br>
The dark gray fields have an odd binary digit sum, and also form a permuted binary Walsh matrix.<br>
A closer look at these five permutations can be found <a href="https://en.wikiversity.org/wiki/Walsh_permutation;_nimber_multiplication;_patterns" class="extiw" title="v:Walsh permutation; nimber multiplication; patterns"><b>here</b></a>.
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<table class="wikitable" style="text-align: center;"><tbody><tr><th colspan="4">Image set <a href="//commons.wikimedia.org/wiki/Category:Operation_tables_with_binary_digits_(16%C3%9716_with_dual_matrices)" title="Category:Operation tables with binary digits (16×16 with dual matrices)">Operation tables with binary digits (16×16 with dual matrices)</a>
</th></tr><tr><td><a href="//commons.wikimedia.org/wiki/File:0...15_AND.svg" class="image"><img alt="0...15 AND.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/48/0...15_AND.svg/160px-0...15_AND.svg.png" decoding="async" width="160" height="200" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/4/48/0...15_AND.svg/240px-0...15_AND.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/4/48/0...15_AND.svg/320px-0...15_AND.svg.png 2x" data-file-width="1127" data-file-height="1407"></a>
</td><td><a href="//commons.wikimedia.org/wiki/File:Nimbers_0...15_multiplication.svg" class="image"><img alt="Nimbers 0...15 multiplication.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nimbers_0...15_multiplication.svg/160px-Nimbers_0...15_multiplication.svg.png" decoding="async" width="160" height="200" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nimbers_0...15_multiplication.svg/240px-Nimbers_0...15_multiplication.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nimbers_0...15_multiplication.svg/320px-Nimbers_0...15_multiplication.svg.png 2x" data-file-width="1127" data-file-height="1407"></a>
</td><td><a href="//commons.wikimedia.org/wiki/File:0...15_times_mod.svg" class="image"><img alt="0...15 times mod.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/0...15_times_mod.svg/160px-0...15_times_mod.svg.png" decoding="async" width="160" height="200" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/0...15_times_mod.svg/240px-0...15_times_mod.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/0...15_times_mod.svg/320px-0...15_times_mod.svg.png 2x" data-file-width="1127" data-file-height="1407"></a>
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<td><a href="//commons.wikimedia.org/wiki/User:Watchduck" title="User:Watchduck">Watchduck</a><br><span style="color: gray; font-size: 80%;">You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".</span>
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