The kerror linear complexity distribution for 2nperiodic binary sequences
Abstract
The linear complexity and the kerror 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 kerror linear complexity distribution of 2 nperiodic binary sequences in this paper based on Games–Chan algorithm. First, for k=2,3, the complete counting functions for the kerror linear complexity of 2 nperiodic binary sequences (with linear complexity less than 2n) are characterized. Second, for k=3,4, the complete counting functions for the kerror linear complexity of 2 nperiodic binary sequences with linear complexity 2n are presented. Third, as a consequence of these results, the counting functions for the number of 2 nperiodic binary sequences with the kerror linear complexity for k=2 and 3 are obtained.
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