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Characterization of almost perfect nonlinear functions in terms of subfunctions. (English. Russian original) Zbl 1409.94939
Discrete Math. Appl. 26, No. 4, 193-202 (2016); translation from Diskretn. Mat. 27, No. 3, 3-16 (2015).
Summary: The paper is concerned with combinatorial description of almost perfect nonlinear functions (APN-functions). A complete characterization of \(n\)-place APN-functions in terms of \((n-1)\)-place subfunctions is obtained. An \(n\)-place function is shown to be an APN-function if and only if each of its \((n-1)\)-place subfunctions is either an APN-function or has the differential uniformity 4 and the admissibility conditions hold. A detailed characterization of 2, 3 or 4-place APN-functions is presented.

MSC:
94B25 Combinatorial codes
06E30 Boolean functions
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References:
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