摘要：

k错线性复杂度度量伪随机序列的稳定性,而关键错误线性复杂度分布能够对k错线性复杂度下降点进行描述。使用方体理论和筛选法研究k错线性复杂度具有第二下降点(关键点)的周期序列。通过分析错线性复杂度第一下降点k=4且第二下降点k′=6的2 ⁿ周期序列,给出序列线性复杂度和第一下降点线性复杂度之间的约束条件,得到第二下降点线性复杂度所有可能的取值形式。推导出在已知序列第一下降点线性复杂度和第二下降点线性复杂度情况下二元序列的计数公式。分析结果表明,该方法可研究具有第三下降点(关键点)的周期序列。

关键词: k错线性复杂度, 关键错误线性复杂度分布, 第二下降点, 方体理论, 筛选法

Abstract:

The k-error linear complexity is used as an important stability index of pseudorandom sequences,and the critical error linear complexity distribution characterize the descent point of k-error linear complexity.This paper studies the 2 ⁿ-periodic binary sequences that k-error linear complexity with second descent point (critical point) via cube theory and sieve method.By analyzing the k-error linear complexity with first descent point k=4 and second descent point k′ =6,the relationship between linear complexity of sequences and linear complexity of the first descent point is established,being given the possible value forms of the first descent point linear complexity.It obtains the counting functions of periodic binary sequences when being given first descent point linear complexity and second descent point linear complexity.Analysis result shows that periodic binary sequences can be studied with third descent point (critical point) of k-error linear complexity by the same methods.

Key words: k-error linear complexity, critical error linear complexity distribution, second descent point, cube theory, sieve method

中图分类号: 

• TP309