期刊名称：International Journal of Security and Its Applications
印刷版ISSN：1738-9976
出版年度：2016
卷号：10
期号：7
页码：169-184
DOI：10.14257/ijsia.2016.10.7.15
出版社：SERSC
摘要：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 2 n , 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 2 n 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 2 n -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 2 n -periodic binary sequences with the given k-error linear complexity profile. Consequently, the complete counting formula of 2 n -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.
关键词：Periodic sequence; linear complexity; k-error linear complexity; cube ; theory
