Geodesic
On~degree of~nonlinearity of~the~coordinate polynomials for~a~product of transformations of~a~binary vector space
Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 2, pp. 74-91

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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 with respect to 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. Tab. 1, bibliogr. 18.
Mots-clés : coordinate polynomial of transformation, maximal monomial of a polynomial
Keywords: degree of a polynomial. 
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     author = {V. M. Fomichev},
     title = {On~degree of~nonlinearity of~the~coordinate polynomials for~a~product of transformations of~a~binary vector space},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {74--91},
     publisher = {mathdoc},
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     year = {2021},
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V. M. Fomichev. On~degree of~nonlinearity of~the~coordinate polynomials for~a~product of transformations of~a~binary vector space. Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 2, pp. 74-91. http://geodesic.mathdoc.fr/item/DA_2021_28_2_a3/