Category:4-ary Zhegalkin indices in 16-cube matrix; great principalities; with entries in top row

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This is a non-diffusing subcategory of 4-ary Zhegalkin indices in 16-cube matrix; great principalities.
Its content is here, but also in the parent, or its subcategories. (See explanation on Wikipedia.)
3-ary (4) 4-ary (20) great principalities with entries on diagonal   (related to patron dominions)
3-ary (4) 4-ary (22) in top row   (related to patron principalities)


The following 22 (of 272) great principalities contain Boolean functions whose Zhegalkin indices are 0 in the less significant half of bits:
[0, 2, 8, 10, 40, 42, 128, 138, 168, 552, 554, 642, 648, 682, 2178, 2184, 2208, 2722, 10368, 10378, 10408, 10922]
They are in the top row of the 256×256 matrix. Their positions on it are shown in a 16×16 matrix.

The 16×16 matrices show a relationship to the Zhegalkin indices of 3-ary principalities. Each one is indicated by the small king index.
The entries in a 16×16 matrix are either evil or odious. (See the odious pattern.) They form pairs that differ only in the most significant bit.
The combined entries of these two matrices form the transpose of the 16×16 matrix shown on the left.



small
faction
size 		small king
small king
index 		Zhegalkin indices
of great principality
1 0
0
26752
104
3 1632
6
28384
110
4 5760
22
10920
42
6 2176
8
3808
14
12 680
2
6856
26
11464
44


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