On the number of bent functions from iterative constructions: lower bounds and hypotheses Full article
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Advances in Mathematics of Communications
ISSN: 1930-5346 , E-ISSN: 1930-5338 |
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| Output data | Year: 2011, Volume: 5, Number: 4, Pages: 609-621 Pages count : 13 DOI: 10.3934/amc.2011.5.609 | ||
| Tags | Asymptotic value; Bent function; Bent sum decomposition; Iterative construction; Monte-Carlo methods | ||
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Abstract:
In the paper we study lower bounds on the number of bent func- tions that can be obtained by iterative constructions, namely by the construc- tion proposed by A. Canteaut and P. Charpin in 2003. The number of bent iterative functions is expressed in terms of sizes of nite sets and it is shown that evaluation of this number is closely connected to the problem of decom- posing Boolean function into sum of two bent functions. A new lower bound for the number of bent iterative functions that is supposed to be asymptotical- ly tight is given. Applying Monte{Carlo methods the number of bent iterative functions in 8 variables is counted. Based on the performed calculations sever- al hypotheses on the asymptotic value of the number of all bent functions are formulated.
Cite:
Tokareva N.
On the number of bent functions from iterative constructions: lower bounds and hypotheses
Advances in Mathematics of Communications. 2011. V.5. N4. P.609-621. DOI: 10.3934/amc.2011.5.609 WOS Scopus OpenAlex
On the number of bent functions from iterative constructions: lower bounds and hypotheses
Advances in Mathematics of Communications. 2011. V.5. N4. P.609-621. DOI: 10.3934/amc.2011.5.609 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000296590400004 |
| Scopus: | 2-s2.0-84975247315 |
| OpenAlex: | W2067550262 |