, Volume 42, Issue 2, pp 181-193
Date: 14 Nov 2006

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

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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 \({\mathbb{F}_{p}}\) .

communicated by D. Jungnickel.