若干二元周期序列的紧错线性复杂度

Tight error linear complexity of periodic binary sequences

综合线性复杂度、k错线性复杂度、k错线性复杂度曲线和最小错误minerro(rS)的概念,提出m紧错线性复杂度的概念。序列S的m紧错线性复杂度是一个二元组(km,LCm)。序列S的k错线性复杂度曲线的第m个跃变点对应的km值和对应km错线性复杂度LCm,称为序列S的m紧错线性复杂度。通过使用简洁的cost二维结构,给出了周期为2n的二元序列的紧错线性复杂度算法,并证明具有Stamp-Martin模式的线性复杂度算法均可以简单地推广为求紧错线性复杂度的算法。与现有k错线性复杂度算法不同,该算法中省去了原来序列元素的运算。在王-张-肖算法基础上,通过使用cost二维结构,给出了周期为pn的二元序列的紧错线性复杂度算法,其中p是一个素数,2是一个模p2的本原根。

Based on the earlier notions of linear complexity,k-error linear complexity,k-error linear complexity profile and minerror,the concept of m-tight error linear complexity is presented to study the stability of the linear complexity of sequences. The m-tight error linear complexity of sequence S is defined as a two tuple （km,LCm）,which is the m-th jump point of the k-error linear complexity profile of sequence S.An algorithm is given for the m-tight error linear complexity of binary sequences with period 2n by using the modified cost different from that used in the Stamp-Martin algorithm.The new algo-rithm is free of computations relating the sequence elements.Based on the Wang-Zhang-Xiao algorithm,an efficient algorithm for computing m-tight error linear complexity of binary sequences with period pn is given,where p is a prime and 2 is a primitive root modulus p2.