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Thin Sidon sets and the nonlinearity of vectorial Boolean functions

· 2022 · math.CO · arXiv 2212.05887

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abstract

The vectorial nonlinearity of a vector valued function is its distance from the set of affine functions. In 2017, Liu, Mesnager and Chen conjectured a general upper bound for the vectorial linearity. Recently, Carlet proved a lower bound in terms of the differential uniformity. In this paper, we improve Carlet's lower bound. Our method is elementary, it relies on the fact that the level sets of an APN functions are Sidon sets. We give a survey on Sidon sets in elementary abelian 2-groups. We study the completeness problem of Sidon sets obtained from hyperbolas and ellipses of the finite affine plane.

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Cardinalities of $g$-difference sets

math.CO · 2025-01-20 · conditional · novelty 6.0

For each fixed g, η_g(n)/√n converges to a positive finite limit, and α_g(n) = (1 + o_g(1))√(gn).

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  • Cardinalities of $g$-difference sets math.CO · 2025-01-20 · conditional · none · ref 23 · internal anchor

    For each fixed g, η_g(n)/√n converges to a positive finite limit, and α_g(n) = (1 + o_g(1))√(gn).