Abstract:
We consider some properties of the coordinate sequences of
linear recurrences over Galois rings which characterize the possibility
of regarding them as pseudo-random sequences. We study the periodicity
properties, linear complexity and frequency characteristics of these
sequences. Up to now, these parameters have been studied mainly in the case
when the linear recurring sequence has maximal possible period. We
investigate the coordinate sequences of linear recurrences of not
necessarily maximal period. We obtain sharpened and generalized
estimates for the number of elements and $r$-patterns on the cycles and
intervals of these sequences.
Keywords:Galois rings, linear recurring sequences, distribution of elements
in sequences, coordinate sequences, exponential sums.
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