In this paper, the definition of multl-output partially Bent functions is presented and some properties are discussed. Then the relationship between multi-output partially Bent functions and multi-output Bent function...In this paper, the definition of multl-output partially Bent functions is presented and some properties are discussed. Then the relationship between multi-output partially Bent functions and multi-output Bent functions is given in Theorem 4, which includes Walsh spectrum expression and function expression. This shows that multi-output partially Bent functions and multi-output Bent functions can define each other in principle. So we obtain the general method to construct multi-output partially Bent functions from multi-output Bent functions.展开更多
Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardwa...Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardware circuit and the soflware program flow chart of the SW/SFH PN code generator are also given,which is based on generalized Bent function sequence generator by using a single chip mlcrocomputer.展开更多
Based on the theory of quadratic forms over finite fields, a new construction of semi-bent and bent functions is presented. The proposed construction has a cascaded characteristic. Some previously known constructions ...Based on the theory of quadratic forms over finite fields, a new construction of semi-bent and bent functions is presented. The proposed construction has a cascaded characteristic. Some previously known constructions of semi-bent and bent functions are special cases of the new construction.展开更多
By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions,and by the Hamming weight of homogenousBoolean function,it is proved that there exist no...By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions,and by the Hamming weight of homogenousBoolean function,it is proved that there exist no homogeneous bent functions ofdegree in in n=2mvariables for m>3.展开更多
This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,...This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,and Applications”.With respect to classical Finite Elements Methods,Trefftz methods are unconventional methods because of the way the basis functions are generated.Trefftz discontinuous Galerkin(TDG)methods have recently shown potential for numerical approximation of transport equations[6,26]with vectorial exponential modes.This paper focuses on a proof of the approximation properties of these exponential solutions.We show that vectorial exponential functions can achieve high order convergence.The fundamental part of the proof consists in proving that a certain rectangular matrix has maximal rank.展开更多
A class of semi-bent functions with an even number of variables is constructed by using the values of Kloosterman sums.These semi-bent functions are Boolean functions with four trace terms.Moreover,it is shown that th...A class of semi-bent functions with an even number of variables is constructed by using the values of Kloosterman sums.These semi-bent functions are Boolean functions with four trace terms.Moreover,it is shown that the algebraic degrees of the new semi-bent functions attain the maximum values.展开更多
基金Supported by State Key Laboratory of InformationSecurity Opening Foundation(01-02) the Doctorate Foundation ofInstitute of Information Engineering (YP20014401)HenanInno-vation Project for University Prominent Research Talents(2003KJCX008)
文摘In this paper, the definition of multl-output partially Bent functions is presented and some properties are discussed. Then the relationship between multi-output partially Bent functions and multi-output Bent functions is given in Theorem 4, which includes Walsh spectrum expression and function expression. This shows that multi-output partially Bent functions and multi-output Bent functions can define each other in principle. So we obtain the general method to construct multi-output partially Bent functions from multi-output Bent functions.
文摘Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardware circuit and the soflware program flow chart of the SW/SFH PN code generator are also given,which is based on generalized Bent function sequence generator by using a single chip mlcrocomputer.
基金The Starting Research Projects for Young Teachers of Southwest Jiaotong University (No.2007Q090)
文摘Based on the theory of quadratic forms over finite fields, a new construction of semi-bent and bent functions is presented. The proposed construction has a cascaded characteristic. Some previously known constructions of semi-bent and bent functions are special cases of the new construction.
基金Supported by the National Natura1 Science Founda—tion of China(60373087,60473023,66973034)the National High-Technology Research and Development Plan of China(2002AA41051)the Ph D Programs Foundation of Ministry of Education of China(20020486046)
文摘By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions,and by the Hamming weight of homogenousBoolean function,it is proved that there exist no homogeneous bent functions ofdegree in in n=2mvariables for m>3.
文摘This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,and Applications”.With respect to classical Finite Elements Methods,Trefftz methods are unconventional methods because of the way the basis functions are generated.Trefftz discontinuous Galerkin(TDG)methods have recently shown potential for numerical approximation of transport equations[6,26]with vectorial exponential modes.This paper focuses on a proof of the approximation properties of these exponential solutions.We show that vectorial exponential functions can achieve high order convergence.The fundamental part of the proof consists in proving that a certain rectangular matrix has maximal rank.
基金Supported by the National Natural Science Foundation of China (60773002)the National High Technology Research and Development Program of China (863 Program) (2007AA01Z472)
文摘A class of semi-bent functions with an even number of variables is constructed by using the values of Kloosterman sums.These semi-bent functions are Boolean functions with four trace terms.Moreover,it is shown that the algebraic degrees of the new semi-bent functions attain the maximum values.
