Some New Results on the Cross Correlation of $m$ -Sequences
Some New Results on the Cross Correlation of $m$ -Sequences
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DOI：
10.1109/tit.2014.2311113
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发表时间：
2013-09
影响因子：
2.5
通讯作者：
Zhang Tao;Shuxing Li;Tao Feng;G. Ge
中科院分区：
文献类型：
--
作者：
Zhang Tao;Shuxing Li;Tao Feng;G. Ge
考虑到33r-1时期的三元序列，我们确定了M-S序列之间的跨相关性及其分解的序列。 32R + 2，其中GCD（R，3）= 1。同时，对于22LM -1的二进制M序列，我们对分解D =（22LM -1）/（2M + 1）进行初始投资2s，l ≥2个<s <s <s <;
The determination of the cross correlation between an m-sequence and its decimated sequence has been a longstanding research problem. Considering a ternary m-sequence of period 33r - 1, we determine the cross correlation distribution for decimations d = 3r + 2 and d = 32r + 2, where gcd(r, 3) = 1. Meanwhile, for a binary m-sequence of period 22lm - 1, we make an initial investigation for the decimation d = (22lm - 1)/(2m + 1) + 2s, where l ≥ 2 is even and 0 <; s <; 2m - 1. It is shown that the cross correlation takes at least four values. Furthermore, we confirm the validity of two famous conjectures due to Sarwate et al. and Helleseth in this case.