Sidelnikov-Lempel-Cohn-Eastman序列的移位不等式
Shift-Inequivalent Decimations of the Sidelnikov-Lempel-Cohn-Eastman Sequences
摘要：
我们考虑了Sidelnikov-Lempel-Cohn-Eastman（SLCE）序列的移位不等价抽取的最大集合的问题（以及确定与这些序列相关的几乎差集的乘子群的等价问题）.给出了一个剩余是SLCE几乎差集的乘子的数值必要条件。利用我们的必要条件，证明了如果$p$是奇素数，且$S$是$\mathbb{F}_p,$上的SLCE几乎差集，则$S$的乘子群是平凡的.因此，对于每个奇素数$p,$，我们得到一族$ϕ(p-1)$移位不等式平衡周期序列（其中$ϕ$是Euler-Totient函数），每个序列具有周期$p-1$和几乎完美的自相关。
英文摘要：
We consider the problem of finding maximal sets of shift-inequivalent decimations of Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences (as well as the equivalent problem of determining the multiplier groups of the almost difference sets associated with these sequences). We derive a numerical necessary condition for a residue to be a multiplier of an SLCE almost difference set. Using our necessary condition, we show that if $p$ is an odd prime and $S$ is an SLCE almost difference set over $\mathbb{F}_p,$ then the multiplier group of $S$ is trivial. Consequently, for each odd prime $p,$ we obtain a family of $ϕ(p-1)$ shift-inequivalent balanced periodic sequences (where $ϕ$ is the Euler-Totient function) each having period $p-1$ and nearly perfect autocorrelation.
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