Sidon sets, thin sets, and the nonlinearity of vectorial Boolean functions
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 established a lower bound in terms of differential uniformity. In this paper, we i...
Elmentve itt :
| Szerző: | |
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2025
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| Sorozat: | JOURNAL OF COMBINATORIAL THEORY SERIES A
212 |
| Tárgyszavak: | |
| doi: | 10.1016/j.jcta.2024.106001 |
| mtmt: | 35664827 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/37462 |
| Tartalmi kivonat: | 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 established a lower bound in terms of differential uniformity. In this paper, we improve Carlet's lower bound. Our approach is based on the fact that the level sets of a vectorial Boolean function are thin sets. In particular, level sets of APN functions are Sidon sets, hence the Liu-Mesnager-Chen conjecture predicts that in F2n, there should be Sidon sets of size at least 2n/2+1 for all n. This paper provides an overview of the known large Sidon sets in F2n, and examines the completeness of the large Sidon sets derived from hyperbolas and ellipses of the finite affine plane. © 2024 Elsevier Inc. |
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| Terjedelem/Fizikai jellemzők: | 21 |
| ISSN: | 0097-3165 |