Geodesic
On a nonlinearity degree definition for a discrete function on a cyclic group
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 26-27.

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An additive approach is proposed to the definition of the nonlinearity degree of a discrete function on a cyclic group. For elementary abelian groups, this notion is equivalent to ordinary “multiplicative” one. For polynomial functions on a ring of integers $\bmod \,p^n$, this notion is equivalent to minimal degree of a polynomial. It is shown that the nonlinearity degree 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: nonlinearity degree, discrete functions. 
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A. V. Cheremushkin. On a nonlinearity degree definition for a discrete function on a cyclic group. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 26-27. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a12/

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