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On the properties of generalized cyclotomic binary sequences of period 2p~m

机译：关于期间2p〜m的广义紧动二元序列性质

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摘要

Xiao, Zeng, Li and Helleseth proposed new generalized cyclotomic binary sequences s(infinity) of period p(m) and showed that these sequences are almost balanced and have very large linear complexity if p is a non-Wieferich prime and m = 2. Wu, Xu, Chen and Ke determined the values of the k-error linear complexity for m = 2 in terms of the theory of Fermat quotients and the results indicated that sequences s infinity have good stability. Edemskiy, Li, Zeng and Helleseth studied the linear complexity of s infinity for general integers m = 2. Furthermore, Ouyang and Xie constructed new 2pm-periodic binary sequences (s) over cap (infinity) and (s) over tilde (infinity) and proved that the sequences (s) over tilde (infinity) and (s) over cap (infinity) are of high linear complexity when m = 2. In this paper we shall show that despite a high linear complexity the sequences s(infinity), (s) over cap (infinity) and (s) over tilde (infinity) have some undesirable features which may not suggest them for cryptography. The properties of multiplicative character sums modulo pm play an important role in the proof of this paper.
机译：肖，曾，李和地狱提出了新的全透过的时期p（m）的全透过的 - 无穷大，并显示出这些序列几乎是平衡的，并且如果p是非Wieferich素和m = 2，则具有非常大的线性复杂性。 Wu，Xu，Chen和Ke确定了Fermat推源理论的M = 2的K误差线性复杂度的值，结果表明序列的无限远具有良好的稳定性。 Edemskiy，Li，Zeng和Helleseth研究了一般整数的SIFINITY的线性复杂性M = 2.此外，Ouyang和谢在TILD（无限远处）上（无限）构建了新的2 pm-periodic二进制序列和（Infinity）并证明，当M = 2时，在帽（无穷大）上的序列（无穷大）和（Infinity）的序列具有高线性复杂性，尽管序列S（Infinity）的高线性复杂性，但仍显示出现。 （s）上帽（无穷大）和横梁（无穷大）具有一些不希望的特征，这可能不建议他们加密。乘法字符和Modulo PM的属性在本文证明中发挥着重要作用。

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