The characterization of 2n-periodic binary sequences with fixed 1-error linear complexity

Authors:
Fang-Wei Fu;Harald Niederreiter;Ming Su
Affiliations:
Temasek Laboratories, National University of Singapore, Singapore, Republic of Singapore;Department of Mathematics, National University of Singapore, Singapore, Republic of Singapore;Department of Mathematics, Nankai University, Tianjin, P.R. China
Venue:
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Year:
2006

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Abstract

The 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.