MAKE A MEME View Large Image Walsh spectrum (polynomial).svg A 3-ary Boolean function <math>f x_1 ~x_2 ~x_3 </math><br> can be expressed by means of the Walsh spectrum <math> r_0 ~r_1 ~r_2 ~r_3 ~r_4 ~r_5 ~r_6 ~r_7 </math><br> as an arithmetical polynomial <math>f~ x_1 ...
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Keywords: 1010 0110 Walsh spectrum (polynomial).svg A 3-ary Boolean function <math>f x_1 ~x_2 ~x_3 </math><br> can be expressed by means of the Walsh spectrum <math> r_0 ~r_1 ~r_2 ~r_3 ~r_4 ~r_5 ~r_6 ~r_7 </math><br> as an arithmetical polynomial <math>f~ x_1 x_2 x_3 ~~~~ ~~~~\tfrac 1 8 ~~\bigg ~~r_0 + r_1 -1 x_1 + r_2 -1 x_2 + r_3 -1 x_1 \oplus x_2 </math><br> <math>+ r_4 -1 x_3 + r_5 -1 x_1 \oplus x_3 + r_6 -1 x_2 \oplus x_3 + r_7 -1 x_1 \oplus x_2 \oplus x_3 ~~\bigg </math> <math>~\oplus~</math> stands for the modulo-2 addition Compare Definition 8 page 2 of the PDF in http //matwbn icm edu pl/ksiazki/amc/amc13/amc13413 pdf The spectral test of the Boolean function linearity by P Porwik own mate2code Walsh spectrum of 3-ary Boolean functions Walsh matrix of order 8
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