Remarks on the k-error linear complexity of pn-periodic sequences

Recently the first author presented exact formulas for the number of 2n-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 2n-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 pn-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 pn-periodic sequences over $${\mathbb{F}_{p}}$$ .