On a nonlinearity degree definition for a discrete function on a cyclic group
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.
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Keywords
дискретные функции, степень нелинейности, nonlinearity degree, discrete functionsAuthors
| Name | Organization | |
| Cheremushkin A. V. | Institute of Cryptography, Telecommunications and Informatics (Moscow) | avc238@mail.ru |
References
Черемушкин А. В. Аддитивный подход к определению степени нелинейности дискретной функции // Прикладная дискретная математика. 2010. №2(8). С. 22-33.
Keller G. and Olson F. Counting polynomial functions (mod pn) // Duke Math. J. 1968. V. 35. P. 835-838.
Chen Z. On polynomial functions from Zni x Zn2 x.. Znr to Zm // Discrete Math. 1996. V.162. P. 67-76.
Черемушкин А. В. Аддитивный подход к определению степени нелинейности дискретной функции на циклической группе примарного порядка // Прикладная дискретная математика. 2013. №2(20). С. 26-38.
