Two new fixed polarity linear Kronecker transforms executed over GF(3) are introduced in this article. Both transforms are based on recursive equations using Kronecker products what allows to obtain simple corresponding fast transforms and very regular butterfly diagrams. The computational costs to calculate the new pair of transforms and their experimental comparison with ternary Reed–Muller t...

As classes of AND-EXOR expressions, PPRMs, FPRMs, and ESOPs are well-known. In this paper, a new class of AND-EXOR expressions, Double Fixed-Polarity Reed-Muller Expressions (DFPRMs), is proposed. DFPRMs are generalized expressions of FPRMs, and can be the smallest PLA among all the classes of AND-EXOR expressions. We discuss their properties: the relation to other classes, a compact realizatio...

In this article, mutual relations between Haar and ReedMuller spectral and functional domains are presented. The new relations apply to any size of the transform matrices in the form of layered vertical and horizontal Kronecker matrices. They allow the direct conversions between Haar and Reed-Muller functions and their corresponding spectra.

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We compute the number of non-minimal codewords of weight 2dmin in the binary Reed-Muller code.

In this paper we present a new method for Boolean matching of completely specified Boolean functions. The canonical Generalized Reed-Muller forms are used as a powerful analysis tool. Input permutation, input and output negation for matching are handled simultaneously. To reduce the search space for input correspondence, we have developed a method that can detect symmetries of any number of inp...

In this article, a new algorithm that takes the truth vector of a 5-valued function as its input and proceeds to generate all of the function’s fixed polarity Reed-Muller (FPRM) spectral coefficient vectors one by one in a certain sequence is presented. The experimental results for this algorithm are compared with other methods and it was found that it is more efficient than other methods for s...

We give a new proof of Delsarte, Goethals and Mac williams theorem on minimal weight codewords of generalized Reed-Muller codes published in 1970. To prove this theorem, we consider intersection of support of minimal weight codewords with affine hyperplanes and we proceed by recursion.

HERMAN Joseph Muller—Joe, as he preferred to be called in his later life—is best known for his discovery of X-ray mutagenesis (Figure 1). Important as this is, it is but a tiny fraction of his work. In his introduction to Muller’s collected papers (Muller 1962, p. v), Joshua Lederberg wrote: ‘‘It is not easy to find an original thought in biological theory that has not, in some way, been antici...