Abstract
Traditional global stability measure for sequences is hard to determine because of large search space. We propose the k-error linear complexity with a zone restriction for measuring the local stability of sequences. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods $$2^n$$
2
n
, or $$2^v r$$
2
v
r
(r odd prime and 2 is primitive modulo r), or $$2^v p_1^{s_1} \cdots p_n^{s_n}$$
2
v
p
1
s
1
⋯
p
n
s
n
($$p_i$$
p
i
is an odd prime and 2 is primitive modulo $$p_i^2$$
p
i
2
, where $$1\le i \le n$$
1
≤
i
≤
n
) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary $$2^n$$
2
n
-periodic binary sequence.
On $k$-error linear complexity of pseudorandom binary sequences derived from Euler quotients
