Depth, ultimate period, and distribution of sequences of period $p^r-1$

Min Zeng; Yuan Luo

8th International Conference on Communications and Networking in China

Research Article

Depth, ultimate period, and distribution of sequences of period $p^r-1$

Cite: BibTeX Plain Text

@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

Min Zeng¹^,*, Yuan Luo¹

1: Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai

*Contact email: inform_code@sjtu.edu.cn

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.

Keywords: depth difference ultimately periodic sequence distribution

Published: 2013-11-14
Publisher: IEEE

: http://dx.doi.org/10.1109/ChinaCom.2013.6694721