Remarks on the k-error linear complexity of p n -periodic sequences

Abstract

Recently the first author presented exact formulas for the number of 2 n -periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k ? 2, of a random 2 n -periodic binary sequence. A crucial role for the analysis played the Chan---Games algorithm. We use a more sophisticated generalization of the Chan---Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for p n -periodic sequences over $${\mathbb{F}_{p, p}}$$ prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of p n -periodic sequences over $${\mathbb{F}_{p}}$$ .