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| In this paper, by investigating vector $emph{ extbf{s}}in F_q$ of length $n$ (or equivalent sequences of period $n$) with infinite third depth, and thecyclic-left-shift-difference operator emph{ extbf{E}}-emph{ extbf{1}} on $emph{ extbf{s}}$, 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{ extbf{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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| Keywords:Depth, Difference, Distribution, Ultimately periodic sequences |
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