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On q-ary Bent and Plateaued Functions
- Source :
- Des. Codes Cryptogr. 88(10), 2037-2049 (2020)
- Publication Year :
- 2019
-
Abstract
- We obtain the following results. For any prime $q$ the minimal Hamming distance between distinct regular $q$-ary bent functions of $2n$ variables is equal to $q^n$. The number of $q$-ary regular bent functions at the distance $q^n$ from the quadratic bent function $Q_n=x_1x_2+\dots+x_{2n-1}x_{2n}$ is equal to $q^n(q^{n-1}+1)\cdots(q+1)(q-1)$ for $q>2$. The Hamming distance between distinct binary $s$-plateaued functions of $n$ variables is not less than $2^{\frac{s+n-2}{2}}$ and the Hamming distance between distinctternary $s$-plateaued functions of $n$ variables is not less than $3^{\frac{s+n-1}{2}}$. These bounds are tight. For $q=3$ we prove an upper bound on nonlinearity of ternary functions in terms of their correlation immunity. Moreover, functions reaching this bound are plateaued. For $q=2$ analogous result are well known but for large $q$ it seems impossible. Constructions and some properties of $q$-ary plateaued functions are discussed.<br />Comment: 14 pages, the results are partialy reported on XV and XVI International Symposia "Problems of Redundancy in Information and Control Systems"
- Subjects :
- Computer Science - Information Theory
94A60, 94C10, 06E30
Subjects
Details
- Database :
- arXiv
- Journal :
- Des. Codes Cryptogr. 88(10), 2037-2049 (2020)
- Publication Type :
- Report
- Accession number :
- edsarx.1911.06973
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10623-020-00761-8