On Boolean functions with several flat spectra
On Boolean functions with several flat spectra
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具有多个平谱的布尔函数
DOI：
10.1007/s12095-018-0309-2
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发表时间：
2019-09
期刊：
影响因子：
--
通讯作者：
Parker Matthew Geoffrey
中科院分区：
文献类型：
--
作者：
Wu Gaofei;Parker Matthew Geoffrey
In this paper, two constructions of Boolean functions which have at least two flat spectra with respect to {H,N}nare proposed. Some known results about bent-negabent functions can be seen as special cases of our results. Furthermore, some lower bounds on the numbers of flat spectra of Boolean functions with respect to {H,N}nor {I,N}nare given. In particular, we show that any Maiorana-McFarland bent function ofn(neven) variables has at leastflat spectra with respect to {H,N}n. Finally, following the work by Riera, Petrides, and Parker, we develop recursive formulae for the numbers of flat spectra of some structural quadratics, including star function, star-line function, and star-line-star function.
In this paper, two constructions of Boolean functions which have at least two flat spectra with respect to {H,N}nare proposed. Some known results about bent-negabent functions can be seen as special cases of our results. Furthermore, some lower bounds on the numbers of flat spectra of Boolean functions with respect to {H,N}nor {I,N}nare given. In particular, we show that any Maiorana-McFarland bent function ofn(neven) variables has at leastflat spectra with respect to {H,N}n. Finally, following the work by Riera, Petrides, and Parker, we develop recursive formulae for the numbers of flat spectra of some structural quadratics, including star function, star-line function, and star-line-star function.
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DOI：
10.1017/cbo9780511780448.011
发表时间：
2010-06
期刊：
--
影响因子：
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作者：
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DOI：
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期刊：
Finite Fields Their Appl.
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DOI：
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期刊：
Science China Information Sciences
影响因子：
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DOI：
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发表时间：
2005
期刊：
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影响因子：
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作者：
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通讯作者：
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DOI：
10.1016/b978-0-12-802318-1.00002-9
发表时间：
2015
期刊：
--
影响因子：
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作者：
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N. Tokareva