2011/08/30 by Jianqin Zhou, Wanquan Liu, Zhou, Jianqin +1
Computer Science · Engineering · #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1108.5793
openalex publication_date 2011/08/30 · openalex created_date 2022/10/03 · 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 studying the linear complexity of binary sequences with period 2n, one could convert the computation of k-error linear complexity into finding error sequences with minimal Hamming weight. Based on Games-Chan algorithm, the k-error linear complexity distribution of 2n-periodic binary sequences is investigated in this paper. First, for k=2,3, the complete counting functions on the k-error linear complexity of 2n-periodic balanced 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, as a consequence of these results, the counting functions for the number of 2n-periodic binary sequences with the k-error linear complexity for k = 2 and 3 are obtained. Further more, an important result in a recent paper is proved to be not completely correct.