Abstract:

The kerror linear complexity is an important stability index of pseudorandom sequences. Based on the cube theory and the reverse process of the GamesChan algorithm, we propose an constructive approach for constructing 2nperiodic binary sequences with given kerror linear complexity spectrum. We use the standard cube decomposition algorithm to classify 2nperiodic binary sequences with the kerror linear complexity of them with the first descent point k=2, the second descent point k′=6 and the third descent point k″=10. We  then discuss the relationship between linear complexity parameters in each category. Finally, we derive the counting formula and construction process on the number of the periodic sequences for each case. In fact, we can construct 2n periodic binary sequence with more descent points of kerror linear complexity by the methods.

Key words: linear complexity, kerror linear complexity spectrum, cube theory, construction approach