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This article is cited in 5 scientific papers (total in 5 papers)
Criteria for maximal nonlinearity of a function over a finite field
V. G. Ryabov NPO «GST»
Abstract:
An $n$-place function over a field with $q$ elements is called maximally nonlinear if it has the greatest nonlinearity among all such functions. Criteria and necessary conditions for maximal nonlinearity are obtained, which imply that, for even $n$, the maximally nonlinear functions are bent functions, but, for $q>2$, the known families of bent functions are not maximally nonlinear. For an arbitrary finite field, a relationship between the Hamming distances from a function to all affine mappings and the Fourier spectra of the nontrivial characters of the function are found.
Keywords:
finite field, nonlinearity, affine function, bent function, Fourier coefficients.
Received: 19.01.2021
Citation:
V. G. Ryabov, “Criteria for maximal nonlinearity of a function over a finite field”, Diskr. Mat., 33:3 (2021), 79–91; Discrete Math. Appl., 33:2 (2023), 117–126
Linking options:
https://www.mathnet.ru/eng/dm1635https://doi.org/10.4213/dm1635 https://www.mathnet.ru/eng/dm/v33/i3/p79
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Abstract page: | 334 | Full-text PDF : | 69 | References: | 39 | First page: | 23 |
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