On the Degree of Nonlinearity of the Coordinate Polynomials for a Product of Transformations of a Binary Vector Space

On the Degree of Nonlinearity of the Coordinate Polynomials for a Product of Transformations of a Binary Vector Space

We construct a nonnegative integer matrix to evaluate the matrix of nonlinearity characteristics for the coordinate polynomials of a product of transformations of a binary vector space. The matrix of the characteristics of the transformation is defined by the degrees of nonlinearity of the derivativ...

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Veröffentlicht in:Journal of applied and industrial mathematics 2021-04, Vol.15 (2), p.212-222
1. Verfasser: Fomichev, V. M.
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Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Polynomials
Transformations (mathematics)
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description We construct a nonnegative integer matrix to evaluate the matrix of nonlinearity characteristics for the coordinate polynomials of a product of transformations of a binary vector space. The matrix of the characteristics of the transformation is defined by the degrees of nonlinearity of the derivatives of all coordinate functions in each input variable. The entries of the evaluation matrix are expressed in terms of the characteristics of the coordinate polynomials of the multiplied transformations. Calculation of the evaluation matrix is easier than calculating the exact values of the characteristics. The estimation method is extended to an arbitrary number of multiplied transformations. Computational examples are given that in particular show the accuracy of the obtained estimates and the domain of their nontriviality.
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subjects Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Polynomials
Transformations (mathematics)
title On the Degree of Nonlinearity of the Coordinate Polynomials for a Product of Transformations of a Binary Vector Space
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