The k-error linear complexity distribution for 2^n-periodic binary sequences |
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Authors: | Jianqin Zhou Wanquan Liu |
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Institution: | 1. Computer Science School, Anhui University of Technology, Ma’anshan, 243002, China 2. Telecommunication School, Hangzhou Dianzi University, Hangzhou, 310018, China 3. Department of Computing, Curtin University, Perth, WA, 6102, Australia
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Abstract: | The linear complexity and the \(k\) -error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the \(k\) -error linear complexity distribution of \(2^n\) -periodic binary sequences in this paper based on Games–Chan algorithm. First, for \(k=2,3\) , the complete counting functions for the \(k\) -error linear complexity of \(2^n\) -periodic binary sequences (with linear complexity less than \(2^n\) ) are characterized. Second, for \(k=3,4\) , the complete counting functions for the \(k\) -error linear complexity of \(2^n\) -periodic binary sequences with linear complexity \(2^n\) are presented. Third, as a consequence of these results, the counting functions for the number of \(2^n\) -periodic binary sequences with the \(k\) -error linear complexity for \(k = 2\) and \(3\) are obtained. |
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