Two new infinite families of APN functions in trivariate form

Note on Budaghyan and Carlet's almost perfect nonlinear functions

H Sun, Q Yue, X Jia - Finite Fields and Their Applications, 2024 - Elsevier
Almost perfect nonlinear (APN) functions have good properties and are widely applied in
sequence design and coding theory. Budaghyan and Carlet (2008)[5] constructed a family of …
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Constructing rotatable permutations of with -homogeneous functions

Y Chi, K Li, L Qu - arXiv preprint arXiv:2401.17094, 2024 - arxiv.org
In the literature, there are many results about permutation polynomials over finite fields.
However, very few permutations of vector spaces are constructed although it has been …
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Changing almost perfect nonlinear functions on affine subspaces of small codimensions

H Taniguchi, A Polujan, A Pott, R Arshad - arXiv preprint arXiv:2501.03922, 2025 - arxiv.org
In this article, we study algebraic decompositions and secondary constructions of almost
perfect nonlinear (APN) functions. In many cases, we establish precise criteria which …
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A proof of a conjecture on trivariate permutations

D Bartoli, M Pal, P Stanica, T Toccotelli - arXiv preprint arXiv:2410.23097, 2024 - arxiv.org
In this note we show (for a large enough dimension of the underlying field) a conjecture of
[C. Beierle, C. Carlet, G. Leander, L. Perrin,{\em A further study of quadratic APN …
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