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Erschienen in:
2006 | OriginalPaper | Buchkapitel
The Characterization of 2 n -Periodic Binary Sequences with Fixed 1-Error Linear Complexity
verfasst von : Fang-Wei Fu, Harald Niederreiter, Ming Su
Erschienen in: Sequences and Their Applications – SETA 2006
Verlag: Springer Berlin Heidelberg
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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 2
n
-periodic binary sequences, Meidl determined the counting function and expected value for the 1-error linear complexity of 2
n
-periodic binary sequences. In this paper, we study the linear complexity and the 1-error linear complexity of 2
n
-periodic binary sequences. Some interesting properties of the linear complexity and the 1-error linear complexity of 2
n
-periodic binary sequences are obtained. Using these properties, we characterize the 2
n
-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 2
n
-periodic binary sequences. Finally, we give new fast algorithms for computing the 1-error linear complexity and locating the error positions for 2
n
-periodic binary sequences.