Sequence Of Linear Complexity Spectrum Analysis

The linear complexity of sequence. (-|s)~n is defined as the length of the shortest linear feedback shift-register that can generate the sequence (-|s)~n, which is a very important parameter to measure the randomness and unpredictable of sequences. The linear complexity of a random sequence should be high enough and its linear complexity profile should follow closely but irregularly the n/2-line. For a finite sequence, it is very important to study its linear complexity, but it is more important to study the changes in the linear complexity of its sub-sequence, that is to say, we should study the linear complexity profile of the sequence.In order to depict the characteristic of the linear complexity profiles of sequences, in this paper, we get the number of sequences with given linear complexity. Given the maximal jump extent of linear complexity D, we also get the number of sequences with given linear complexity L of length n. Furthermore, we get the expected maximal jump extend of sequences with length n, and we also get the expectation and variance of the jump complexity of random sequence of length n and linear complexity L.