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The nonlinearity of these functions is extremely close to the maximum nonlinearity attained by bent functions and it might be the case that this is the highest possible nonlinearity of 1-resilient functions.
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We also identify all the functions whose nonlinearity attains the lower bound.
In this article we improve the lower bound on the maximum nonlinearity of 1-resilient Boolean functions, for n even, by proposing a method of constructing this class of functions attaining the best nonlinearity currently known.
In the table, Δ θ is the average error of the direction of maximum nonlinearity.
In the paper, there are two alternatives for choosing the direction of maximum nonlinearity.
AS and BinoGMF use the same algorithm for computing the direction of maximum nonlinearity.
This causes fewer problems with AS, because AS splits only in the direction of maximum nonlinearity and then re-evaluates the nonlinearity for the resulting components.
This solves the maximum nonlinearity issue for 7-variable functions with any order of resiliency.
The conversion time and maximum nonlinearity are less than 100 μs and 24 ppm, respectively.
The sensors' linearity was 0.62% of maximum nonlinearity over the full range of hand motion.
Such maximum is attained at.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com