Earticle

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.

The periodic estimation method of the PN sequence in DS Signal is researched. It is hard for traditional methods to estimate PN period of DS/SS accurately in the condition of low Signal-to-noise ratio. On the basis of the traditional spectrum reprocessing and the cepstrum method, a PN period estimation method which has integrated serial average with spectrum reprocessing and the cepstrum are put forward to solve this problem and meet the requirements of lower Signal-to-noise ratio. The simulation results show that, when the period of PN sequence is estimated accurately, the cepstrum method has better estimating performance than the spectrum reprocessing method, and the spectral estimation method has lower Signal-to-noise ratio tolerance after improvements.

In this paper, we introduce a class of Moran measures generated by quasi periodic sequences, and consider power decay of the Fourier transforms of this kind of measures.