|
This article is cited in 1 scientific paper (total in 1 paper)
Discrete Functions
Properties of subfunctions of self-dual bent functions
A. V. Kutsenkoab a Novosibirsk State University, Mechanics and Mathematics Department
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
Boolean functions in an even number of variables with flat Walsh — Hadamard spectrum are called bent functions. For every bent function, say $f$, its dual bent function, denoted by $\widetilde{f}$, is uniquely defined. If ${\widetilde{f}=f}$, then $f$ is called self-dual bent, and in the case ${\widetilde{f}=f\oplus 1}$ it is called an anti-self-dual bent. In this paper, we study subfunctions of self-dual bent functions obtained by a fixation of the first and the first two coordinates. We characterize subfunctions in $n-1$ variables considering their Rayleigh quotients. A sufficient condition for all subfunctions in $n-2$ variables to be bent is obtained. We propose new iterative constructions of self-dual bent functions in $n$ variables comprising the usage of bent functions in ${n-4}$ variables. Based on them, a new iterative lower bound on the cardinality of the set of self-dual bent functions is obtained.
Keywords:
self-dual bent function, subfunction, near-bent function, Rayleigh quotient of the Sylvester Hadamard matrix.
Citation:
A. V. Kutsenko, “Properties of subfunctions of self-dual bent functions”, Prikl. Diskr. Mat. Suppl., 2022, no. 15, 26–30
Linking options:
https://www.mathnet.ru/eng/pdma572 https://www.mathnet.ru/eng/pdma/y2022/i15/p26
|
Statistics & downloads: |
Abstract page: | 69 | Full-text PDF : | 30 | References: | 11 |
|