Research Article
Depth, ultimate period, and distribution of sequences of period $p^r-1$
@INPROCEEDINGS{10.1109/ChinaCom.2013.6694721, author={Min Zeng and Yuan Luo}, title={Depth, ultimate period, and distribution of sequences of period \textdollar{}p\^{}r-1\textdollar{}}, proceedings={8th International Conference on Communications and Networking in China}, publisher={IEEE}, proceedings_a={CHINACOM}, year={2013}, month={11}, keywords={depth difference ultimately periodic sequence distribution}, doi={10.1109/ChinaCom.2013.6694721} }- Min Zeng
Yuan Luo
Year: 2013
Depth, ultimate period, and distribution of sequences of period $p^r-1$
CHINACOM
IEEE
DOI: 10.1109/ChinaCom.2013.6694721
Abstract
In this paper, by investigating vector $\emph{\textbf{s}}\in F_q$ of length $n$ (or equivalent sequences of period $n$) with infinite third depth, and the cyclic-left-shift-difference operator \emph{\textbf{E}}-\emph{\textbf{1}} on $\emph{\textbf{s}}$, an ultimate period sequence \SpecialSequence\ is constructed. Some upper bounds on the ultimate period of \SpecialSequence\ and a method to determine the least ultimate period are provided. Furthermore, distributions of vectors \emph{\textbf{s}} with period $n=p^r-1$ ($r>0$), are described in terms of the least ultimate periods of their respective sequences \SpecialSequence.
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