The
k-error linear complexity of periodic sequences is an important security index of stream cipher systems. By using an interesting decomposing approach, we investigate the intrinsic structure for the set of 2
n-periodic binary sequences with fixed complexity measures. For
k ≤ 4, we construct the complete set of error vectors that give the
k-error linear complexity. As auxiliary results we obtain the counting functions of the
k-error linear complexity of 2
n-periodic binary sequences for
k ≤ 4, as well as the expectations of the
k-error linear complexity of a random sequence for
k ≤ 3. Moreover, we study the 2
t-error linear complexity of the set of 2
n-periodic binary sequences with some fixed linear complexity
L, where
t < n-1 and the Hamming weight of the binary representation of 2
n-
L is
t. Also, we extend some results to
pn-periodic sequences over F
p. Finally, we discuss some potential applications.
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