Cube theory and kerror linear complexity profile
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© 2016 SERSC. The linear complexity and kerror linear complexity of a sequence have been used as important measures for keystream strength. In order to study kerror 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 mcubes with the same linear complexity is derived, which is equivalent to the counting formula for kerror vectors. The counting formula of 2nperiodic 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 2nperiodic binary sequences with the given kerror linear complexity profile. Consequently, the complete counting formula of 2nperiodic binary sequences with given kerror linear complexity profile of descent points 2, 4 and 6 is derived. The periodic sequences having the prescribed kerror linear complexity profile with descent points 1, 3, 5 and 7 are also briefly discussed.
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