Geodesic
Efficient Calculation of the Reed-Muller Form by Means of the Walsh Transform
International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) no. 4, pp. 571-579

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The paper describes a spectral method for combinational logic synthesis using the Walsh transform and the Reed-Muller form. A new algorithm is presented that allows us to obtain the mixed polarity Reed-Muller expansion of Boolean functions. The most popular minimisation (sub-minimisation) criterion of the Reed-Muller form is obtained by the exhaustive search of all the polarity vectors. This paper presents a non-exhaustive method for Reed-Muller expansions. The new method allows us to build the Reed-Muller form based on the analysis of Walsh-Hadamard coefficients. The presented method has much less complexity than the procedures which have been applied until now. Both the transforms and the presented Walsh-Hadamard spectral characterization of the Reed-Muller expansion are compared. An analysis of the properties of the spectra obtained from these transforms is made.
Keywords: Reed-Muller coefficients, Walsh coefficients, coefficient distribution, Boolean function, synthesis of Boolean functions
Mots-clés : informatyka 
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     author = {Porwik, P.},
     title = {Efficient {Calculation} of the {Reed-Muller} {Form} by {Means} of the {Walsh} {Transform}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {571--579},
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     number = {4},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2002_12_4_a11/}
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Porwik, P. Efficient Calculation of the Reed-Muller Form by Means of the Walsh Transform. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) no. 4, pp. 571-579. http://geodesic.mathdoc.fr/item/IJAMCS_2002_12_4_a11/