Determine Spectral Coefficients of Boolean Functions by Using Walsh-Rademacher Transform

Abstract

Walsh transform belongs to a class of orthogonal transforms, which used in many problems, like spectral methods. One of these problems is to check the linearity of Boolean functions by means of Walsh spectral technique. Walsh transform can be represented by many ways like,walsh-Hadamard transform (W-H.T) and Walsh-Rademacher transform (W-R.T). Porwik,[4] used Walsh-Hadamard transform to determine the Spectral coefficient of Boolean functions, and used it to investigate the linearity of Boolean functions directly on the basis of Walsh coefficients.