Geodesic
An additive approach to nonlinearity degree of discrete functions on a~primary cyclic group
Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 26-38

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An additive approach to the definition of nonlinearity degree for a discrete function on a cyclic group is proposed. For elementary abelian groups, this notion is equivalent to the ordinary “multiplicative” one. For polynomial functions on the ring of integers $\mod p^n$, this notion is equivalent to the minimal degree of a polynomial. It is proved that the nonlinearity degree on a cyclic group is a finite number if and only if the order of the group is a power of a prime. An upper bound for the nonlinearity degree of functions on a cyclic group of order $p^n$ is given.
Keywords: discrete functions, nonlinearity degree. 
@article{PDM_2013_2_a3,
     author = {A. V. Cheremushkin},
     title = {An additive approach to nonlinearity degree of discrete functions on a~primary cyclic group},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {26--38},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2013_2_a3/}
}
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A. V. Cheremushkin. An additive approach to nonlinearity degree of discrete functions on a~primary cyclic group. Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 26-38. http://geodesic.mathdoc.fr/item/PDM_2013_2_a3/