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- W2942941259 abstract "The associated codes of almost perfect nonlinear (APN) functions have been widely studied. In this paper, we consider more generally the codes associated with functions that have differential uniformity at least begin{document}$ 4 $end{document} . We emphasize, for such a function begin{document}$ F $end{document} , the role of codewords of weight begin{document}$ 3 $end{document} and begin{document}$ 4 $end{document} and of some cosets of its associated code begin{document}$ C_F $end{document} . We give some properties on codes associated with differential uniformity exactly begin{document}$ 4 $end{document} . We obtain lower bounds and upper bounds for the numbers of codewords of weight less than begin{document}$ 5 $end{document} of the codes begin{document}$ C_F $end{document} . We show that the nonlinearity of begin{document}$ F $end{document} decreases when these numbers increase. We obtain a precise expression to compute these numbers, when begin{document}$ F $end{document} is a plateaued or a differentially two-valued function. As an application, we propose a method to construct differentially begin{document}$ 4 $end{document} -uniform functions, with a large number of begin{document}$ 2 $end{document} -to- begin{document}$ 1 $end{document} derivatives, from APN functions." @default.
- W2942941259 created "2019-05-09" @default.
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- W2942941259 date "2019-01-01" @default.
- W2942941259 modified "2023-09-26" @default.
- W2942941259 title "Differential uniformity and the associated codes of cryptographic functions" @default.
- W2942941259 doi "https://doi.org/10.3934/amc.2019036" @default.
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