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Cube Theory and k-error Linear Complexity Profile
Jianqin Zhou,Wanquan Liu,Xifeng Wang 보안공학연구지원센터 2016 International Journal of Security and Its Applicat Vol.10 No.7
The linear complexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2n, a new tool called cube theory is developed. In this paper, we first give a general decomposition approach to decompose a binary sequence with period 2n into some disjoint cubes. Second, a counting formula for m-cubes with the same linear complexity is derived, which is equivalent to the counting formula for k-error vectors. The counting formula of 2n-periodic binary sequences which can be decomposed into more than one cube is also investigated, which extends an important result by Etzion et al.. Finally, we study 2n-periodic binary sequences with the given k-error linear complexity profile. Consequently, the complete counting formula of 2n-periodic binary sequences with given k-error linear complexity profile of descent points 2, 4 and 6 is derived. The periodic sequences having the prescribed k-error linear complexity profile with descent points 1, 3, 5 and 7 are also briefly discussed.
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Zhaoyu Ren,Wei Zhang,Mengke Wang,Haifeng Gao,Huimin Shen,Chunping Wang,Taiguo Liu,Wanquan Chen,Li Gao 한국식물병리학회 2021 Plant Pathology Journal Vol.37 No.5
Tilletia laevis Kühn (syn. Tilletia foetida (Wallr.) Liro.) causes wheat common bunt, which is one of the most devastating plant diseases in the world. Common bunt can result in a reduction of 80% or even a total loss of wheat production. In this study, the characteristics of T. laevis infection in compatible wheat plants were defined based on the combination of scanning electron mi- croscopy, transmission electron microscopy and laser scanning confocal microscopy. We found T. laevis could lead to the abnormal growth of wheat tissues and cells, such as leakage of chloroplasts, deformities, disordered arrangements of mesophyll cells and also thickening of the cell wall of mesophyll cells in leaf tissue. What’s more, T. laevis teliospores were found in the roots, stems, flag leaves, and glumes of infected wheat plants instead of just in the ovaries, as previously reported. The abnormal characteristics caused by T. laevis may be used for early detection of this pathogen instead of molecular markers in addition to providing theoretical insights into T. laevis and wheat interactions for breed- ing of common bunt resistance.
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