An additive approach to nonlinearity degree of discrete functions on a primary cyclic group | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2013. № 2(20).

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 modp ⁿ, this notion is equivalent to the minimal degree of a polynomial. It is proved that the non-linearity 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.