Period-Different $m$-Sequences With at Most Four-Valued Cross Correlation
Period-Different $m$-Sequences With at Most Four-Valued Cross Correlation
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DOI：
10.1109/tit.2009.2021312
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发表时间：
2008-01
影响因子：
2.5
通讯作者：
T. Helleseth;L. Hu;A. Kholosha;Xiangyong Zeng;Nian Li;Wenfeng Jiang
中科院分区：
文献类型：
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作者：
T. Helleseth;L. Hu;A. Kholosha;Xiangyong Zeng;Nian Li;Wenfeng Jiang
本文继承Helleseth， Kholosha, Johansen，和Ness最近的工作，研究了周期为2m - 1的m-序列与更短周期为2n - 1的m-序列对偶数m = 2n的d抽取之间的相互关系。假设d满足d(2l + 1) = 2i （mod 2n - 1）对于某些l > 0和i > 0，证明了根据i和n是否为素数，相互关系取恰好3或4个值。互相关值的分布也完全确定。我们的结果在理论上证实了Ness和Helleseth的数值数据。据推测，除了这里所证明的那些，没有其他的十进制能给出最多四值的互相关。
This paper follows the recent work of Helleseth, Kholosha, Johansen, and Ness to study the cross correlation between an m -sequence of period 2m - 1 and the d-decimation of an m-sequence of a shorter period 2n - 1 for an even number m = 2n. Assuming that d satisfies d(2l + 1) = 2i (mod 2n - 1) for some l > 0 and i > 0, it is proved that the cross correlation takes on either exactly three or four values depending on whether I and n are coprime or not. The distribution of the cross-correlation values is also completely determined. Our results theoretically confirm the numerical data by Ness and Helleseth. It is conjectured that there are no other decimations that give at most four-valued cross correlation apart from the ones proved here.