Abstract
AbstractThe linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, using fast algorithms for computing the linear complexity and the k-error linear complexity of 2n-periodic binary sequences, Meidl determined the counting function and expected value for the 1-error linear complexity of 2n-periodic binary sequences. In this paper, we study the linear complexity and the 1-error linear complexity of 2n-periodic binary sequences. Some interesting properties of the linear complexity and the 1-error linear complexity of 2n-periodic binary sequences are obtained. Using these properties, we characterize the 2n-periodic binary sequences with fixed 1-error linear complexity. Along the way, we obtain a new approach to derive the counting function for the 1-error linear complexity of 2n-periodic binary sequences. Finally, we give new fast algorithms for computing the 1-error linear complexity and locating the error positions for 2n-periodic binary sequences.KeywordsStream cipher systemsPeriodic sequencesLinear complexity k-Error linear complexityCounting functionFast algorithms
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