On a nonlinearity degree definition for a discrete function on a cyclic group | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2013. № 6 (Приложение).

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 mod p , 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 is given.