The Eigenfunction of the Reed-Muller Transformation

Sasao, Tsutomu; Bulter, J T

doi:10.21236/ada604853

Cited by 10 publications

(13 citation statements)

References 16 publications

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“…A truth vector satisfying the equation RM·F = F is an eigenvector of RM with the eigenvalue λ = 1 [5], [7]. To find the eigenvectors, the eigenvalues are needed first, which may be calculated by using the characteristic polynomial.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

On Fixed Points and Cycles in the Reed Muller Domain

Moraga

Stojkovic

Stanković

2008

38th International Symposium on Multiple Valued Logic (Ismvl 2008)

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This paper studies cycles that appear by repeatedly applying the RM transform to a p-valued function. It is shown that there are nontrivial fixed points, which correspond to eigenvectors of the transform and a simple method is proposed to determine the maximum period of n-place functions for a given p. The concept of spectral diversity is introduced, which may be applied to characterize pvalued functions.

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Section: Discussionmentioning

confidence: 99%

“…Eigenvectors of the Reed Muller Transformation for the binary case were studied in [5]. The present paper may be considered a further step in that line of research.…”

Section: Introductionmentioning

confidence: 93%

On Fixed Points and Cycles in the Reed Muller Domain

Moraga

Stojkovic

Stanković

2008

38th International Symposium on Multiple Valued Logic (Ismvl 2008)

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“…The Preparata (Reed-Müller) Transformation (Preparata, 1964;Saluja and Ong, 1979;Green, 1987;1994;Stankovic et al, 1996;Kim et al, 1999;Quintana and Avedillo, 2001;Sasao and Butler, 2007;Rushdi and Ghaleb, 2013) for a Boolean function …”

Section: Preparata Transformationmentioning

confidence: 99%

On Self-Inverse Binary Matrices Over the Binary Galois Field

Rushdi¹

2013

Journal of Mathematics and Statistics

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An important class of square binary matrices over the simplest finite or Galois Field GF(2) is the class of involutory or Self-Inverse (SI) matrices. These matrices are of significant utility in prominent engineering applications such as the study of the Preparata Transformation or the analysis of synchronous Boolean Networks. Therefore, it is essential to devise appropriate methods, not only for understanding the properties of these matrices, but also for characterizing and constructing them. We survey square binary matrices of orders 1, 2 and 3 to identify primitive SI matrices among them. Larger SI matrices are constructed as (a) the direct sum, or (b) the Kronecker product, of smaller ones. Illustrative examples are given to demonstrate the construction and properties of binary SI matrices. The intersection of the sets of SI and permutation binary matrices is studied. We also study higher-order SI binary matrices and describe them via recursive relations or Kronecker products. Our work culminates in an exposition of the two most common representations of Boolean functions via two types of Boolean SI matrices. A better understanding of the properties and methods of constructing SI binary matrices over GF (2) is achieved. A clearer picture is attained about the utility of binary matrices in the representation of Boolean functions

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“…The eigenvector x for any matrix M is calculated using the characteristic equation , where is the eigenvalue for matrix M. The eigenvectors and eigenvalues of RMT follow the definition given below, as mentioned in [7]. The RMT matrix R(n) can be decomposed using the kronecker product as given by (9).…”

Section: Eigen Vector Decomposition Of Reed-muller Transform (Rmt)mentioning

confidence: 99%

“…Since Reed-Muller transform is so widely used, it will be useful to find algorithms to perform its eigen-decomposition. Eigenfunctions of Reed-Muller Transform were introduced by Sasao and Butler in [7]. The work identified three symmetric functions with certain special properties and showed that these symmetric functions can be found among the eigenfunctions of the Reed-Muller transform.…”

Section: Introductionmentioning

confidence: 99%