Criteria for maximal nonlinearity of a function over a finite field
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Vladimir V. Ryabov
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.
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Articles in the same Issue
- Frontmatter
- On the existence of special nonlinear invariants for round functions of XSL-ciphers
- Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants
- Decomposition of polynomials using the shift-composition operation
- Mutually Orthogonal Latin Squares as Group Transversals
- Explicit basis for admissible rules in K-saturated tabular logics
- Criteria for maximal nonlinearity of a function over a finite field
Articles in the same Issue
- Frontmatter
- On the existence of special nonlinear invariants for round functions of XSL-ciphers
- Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants
- Decomposition of polynomials using the shift-composition operation
- Mutually Orthogonal Latin Squares as Group Transversals
- Explicit basis for admissible rules in K-saturated tabular logics
- Criteria for maximal nonlinearity of a function over a finite field
