Abstract
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 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 \({\mathbb{F}_{p}}\) .
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communicated by D. Jungnickel.
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Meidl, W., Venkateswarlu, A. Remarks on the k-error linear complexity of p n-periodic sequences. Des Codes Crypt 42, 181–193 (2007). https://doi.org/10.1007/s10623-006-9029-2
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DOI: https://doi.org/10.1007/s10623-006-9029-2