2011/12/28 by Jianqin Zhou, Jun Liu, Zhou, Jianqin +3 · 2 citations
Computer Science · Engineering · #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #cs.CR #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1112.6047
7 pages
arxiv created 2011/12/28 · openalex publication_date 2011/12/28 · arxiv updated 2011/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, the k-error linear complexity distribution of 2n-periodic binary sequences is investigated based on Games-Chan algorithm. First, for k=2,3, the complete counting functions on the k-error linear complexity of 2n-periodic binary sequences with linear complexity less than 2n are characterized. Second, for k=3,4, the complete counting functions on the k-error linear complexity of 2n-periodic binary sequences with linear complexity 2n are presented. Third, for k=4,5, the complete counting functions on the k-error linear complexity of 2n-periodic binary sequences with linear complexity less than 2n are derived. As a consequence of these results, the counting functions for the number of 2n-periodic binary sequences with the 3-error linear complexity are obtained, and the complete counting functions on the 4-error linear complexity of 2n-periodic binary sequences are obvious.