On the $k$-Error Linear Complexity of $p^{m}$ -Periodic Binary Sequences

In this correspondence, we study the statistical stability properties of p
^m
-periodic binary sequences in terms of their linear complexity and k-error linear complexity, where p is n prime number and 2 is a primitive root modulo p
²
. We show that their linear complexity and k-error linear complexity take a value only from some specific ranges. We then present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity in a new viewpoint different from the approach by Meidl. We also derive the distribution of p
^m
-periodic binary sequences with specific k-error linear complexity. Finally, we get an explicit formula for the expectation value of the k-error linear complexity and give its lower and upper bounds, when k les [p/2].