Further Results on the Distinctness of Decimations of l-sequences
<|reference_start|>Further Results on the Distinctness of Decimations of l-sequences: Let $\underline{a}$ be an \textit{l}-sequence generated by a feedback-with-carry shift register with connection integer $q=p^{e}$, where $ p$ is an odd prime and $e\geq 1$. Goresky and Klapper conjectured that when $ p^{e}\notin \{5,9,11,13\}$, all decimations of $\underline{a}$ are cyclically distinct. When $e=1$ and $p>13$, they showed that the set of distinct decimations is large and, in some cases, all deciamtions are distinct. In this article, we further show that when $e\geq 2$ and$ p^{e}\neq 9$, all decimations of $\underline{a}$ are also cyclically distinct.<|reference_end|>
@article{xu2006further,
    title={Further Results on the Distinctness of Decimations of l-sequences},
    author={Hong Xu and Wen-Feng Qi},
    journal={arXiv preprint arXiv:cs/0601024},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0601024},
    primaryClass={cs.CR}
}