Category:Walsh spectra of 3-ary Boolean functions; families

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examples in a simplified style (cat)

Each of these files shows the Walsh spectra of all Boolean functions in the same family (N-EC).
They are labeled with the clan (NP-EC) the families belong to.

These are matrix multiplications. The factors are to the left and above the result.
The first factor is the family matrix, and the second one a Walsh matrix.

The Walsh spectra (compare Walsh–Hadamard transform) are shown by numbers.
The binary Walsh spectra are shown by the red-white background pattern of the result.
They are obtained by multiplying with a binary Walsh matrix (which is shown by the red-white background of the second factor).

odd edit

Families with odd weight have all 8 possible binary Walsh spectra.
In these images the function corresponding to the all-zeros row is chosen as first row of the family matrix.