2^n-周期二元序列的3-错误序列分布

On the 3 error Sequence Distribution of 2^n- periodic Binary Sequences

线性复杂度和k.-错线性复杂度是度量密钥流序列密码强度的重要指标。为了更好地研究序列的随机性,该文通过将序列的k.-错线性复杂度的计算转化为求Hamming重量最小的错误序列的方法,讨论了序列不同k.-错线性复杂度条件下对应的k.-错误序列的分布情况。基于Games-Chan算法,该文给出了线性复杂度为2n的2n-周期二元序列的3错误序列的计数公式,计算机编程验证了该文方法的正确性。

The linear complexity and the k - error linear complexity of a sequence are used as important measures of keystream strength. By studying linear complexity of binary sequences with period 2^n , it is proposed that the computation of k- error linear complexity can be converted to finding error sequences with minimal Hamming weight. In order to study sequence randomness, the k- error sequences distribution that corresponds with the k- error linear complexity of sequence is discussed. Based on Games-Chan algorithm, for k = 3, the counting functions on the k- error sequences of 2^n- periodic binary sequences with linear complexity 2^n- are derived and the effectiveness is proved with computer programming.