Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But th...Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang（1989, 1990, 1993） by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36（6^13^42^10）, are constructed.展开更多
The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which availab...The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which available encryption matrices are selected. Then, a higher order encryption matrix relating real world application is constructed by means of tensor production method based on selected encryption matrices. The results show that the proposed algorithm can produce a "one-time pad cipher" encryption matrix with high security; and the encryption results have good chaos and auto-correlation with the natural frequency of the plaintext being hidden and homogenized.展开更多
In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKN...In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNSequation is presented.展开更多
基金the National Science Foundations of China(10571045)the National Science Foundations of Henan Province(02243700510211063100)
文摘Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang（1989, 1990, 1993） by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36（6^13^42^10）, are constructed.
基金Supported by the National Natural Science Foundation of China (No. 61173036)
文摘The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which available encryption matrices are selected. Then, a higher order encryption matrix relating real world application is constructed by means of tensor production method based on selected encryption matrices. The results show that the proposed algorithm can produce a "one-time pad cipher" encryption matrix with high security; and the encryption results have good chaos and auto-correlation with the natural frequency of the plaintext being hidden and homogenized.
基金Supported by the National Natural Science Foundation of China under Grant No.10926036the Education Department of Zhejiang Province under Grant No.Y200906909the Zhejiang Provincial Natural Science Foundation of China under Grant No.Y6090172
文摘In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNSequation is presented.
