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Balanced and constant functions as seen by Hadamard

Explore the properties of balanced and constant functions as perceived through Hadamard analysis. Discover the significance of minterms, correlation measure, and local patterns in matrix representations. Gain insights into the unique characteristics of these functions and their relationship with other rows in the matrix.

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Balanced and constant functions as seen by Hadamard

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  1. Balanced and constant functions as seen by Hadamard Ones in map encoded by “-1”, zeros by “1” This is number of minterms “0” in the function Constant 0 This is measure of correlation with other rows of M = Vector V Matrix M Vector S

  2. Balanced and constant functions as seen by Hadamard This is number of minterms “1” in the function Constant 1 This is measure of correlation with other rows of M = Vector V Matrix M Vector S

  3. Balanced and constant functions as seen by Hadamard This means we have half “1” and half “0s” balanced = Vector V Matrix M Vector S

  4. Local patterns for Affine functions cd 00 01 11 10 ab 00 0111 10 a  b  c d 1

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