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| lower bounds on the second order nonlinearity of boolean functions | |
| Li Xuelian; Hu Yupu; Gao Juntao | |
| 2011 | |
| Source | INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
 |
| ISSN | 0129-0541 |
| Volume | 22Issue:6Pages:1331-1349 |
| English Abstract | It is a difficult task to compute the r-th order nonlinearity of a given function with algebraic degree strictly greater than r > 1. Though lower bounds on the second order nonlinearity are known only for a few particular functions, the majority of which are cubic. We investigate lower bounds on the second order nonlinearity of cubic Boolean functions F(x) = Tr(Sigma(m)(l=1)mu(l)x(dl)), where mu(l) is an element of F*(2n), d(l) = 2(il) + 2(jl) + 1, m, i(l) and j(l) are positive integers, n > i(l) > j(l). Furthermore, for a class of Boolean functions G(x) = Tr(Sigma(m)(l=1)mu(l)x(dl)), we deduce a tighter lower bound on the second order nonlinearity of the functions, where mu(l) is an element of F*(2n), d(l) = 2(il gamma) + 2(jl gamma) + 1, i(l) > j(l) and gamma not equal 1 is a positive integer such that gcd(n, gamma) = 1. Lower bounds on the second order nonlinearity of cubic monomial Boolean functions, represented by f(mu)(x) = Tr(mu x(2i+2j+1)), mu is an element of F*(2n), i and j are positive integers such that i > j, were obtained by Gode and Gangopadhvay in 2009. In this paper, we first extend the results of Gode and Gangopadhvay from monomial Boolean functions to Boolean functions with more trace terms. We further generalize and improve the results to a wider range of n. Our bounds are better than those of Gode and Gangopadhvay for monomial functions f(mu)(x). Especially, our lower bounds on the second order nonlinearity of some Boolean functions F(x) are better than the existing ones. |
| Indexed Type | SCI ; CNKI |
| Abstract | 通过实验研究了基于碳纳米管(CNTs)的含油纳米制冷剂(即由制冷剂R113、润滑油VG68和碳纳米管组成的纳米流体)的核态池沸腾换热特性,分析了碳纳米管对含油制冷剂核态池沸腾换热的影响。实验中采用了外径为15~80nm、长度为1.5~10μm的四种碳纳米管。实验的饱和压力为101.3 kPa;热流密度为10~80 kW/m2;纳米油(碳纳米管和润滑油的混合物)的质量分数为0~5%;在纳米油中碳纳米管的质量分数为0~30%。实验结果表明:碳纳米管增强了含油制冷剂的池沸腾换热,在测试工况下换热系数最大可增加61%。当纳米油中碳纳米管浓度为20%不变,纳米油浓度由1%提高到5%时,不同尺寸的碳纳米管对换热系数的增加幅度由27%~59%降低至23%~55%;当纳米油的浓度为1%不变,纳米油中碳纳米管浓度由20%提高到30%时,不同尺寸的碳纳米管对换热系数的增加幅度由27%~59%升高到33%~61%。通过实验获得了基于碳纳米管的含油纳米制冷剂池沸腾换热关联式,关联式的预测值与96%的实验数据偏差在±10%以内。 |
| Keyword | 工程热物理 碳纳米管 关联式 核态池沸腾 润滑油 制冷剂 |
| Department | Li Xuelian Xidian Univ Dept Math Xian 710071 Shannxi Peoples R China. Hu Yupu; Gao Juntao Xidian Univ Minist Educ Key Lab Comp Networks & Informat Secur Xian 710071 Shannxi Peoples R China. Gao Juntao Chinese Acad Sci Inst Software State Key Lab Informat Secur Beijing 100190 Peoples R China. |
| Subject | Computer Science |
| Sponsorship | 973 Project of China2007CB311201; National Natural Science Foundation60833008, 60803149; Fundamental Research Funds for the Central Universities72004295 |
| Language | 英语 |
| WOS ID | WOS:000294809400008 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16076 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Li Xuelian,Hu Yupu,Gao Juntao. lower bounds on the second order nonlinearity of boolean functions[J]. INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE,2011,22(6):1331-1349. |
| APA | Li Xuelian,Hu Yupu,&Gao Juntao.(2011).lower bounds on the second order nonlinearity of boolean functions.INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE,22(6),1331-1349. |
| MLA | Li Xuelian,et al."lower bounds on the second order nonlinearity of boolean functions".INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 22.6(2011):1331-1349. |
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