Geodesic
Frequency characteristics of coordinate sequences of linear recurrences over Galois rings
Izvestiya. Mathematics , Tome 77 (2013) no. 6, pp. 1130-1154

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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. 
@article{IM2_2013_77_6_a2,
     author = {O. V. Kamlovskii},
     title = {Frequency characteristics of coordinate sequences of linear recurrences over {Galois} rings},
     journal = {Izvestiya. Mathematics },
     pages = {1130--1154},
     publisher = {mathdoc},
     volume = {77},
     number = {6},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a2/}
}
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O. V. Kamlovskii. Frequency characteristics of coordinate sequences of linear recurrences over Galois rings. Izvestiya. Mathematics , Tome 77 (2013) no. 6, pp. 1130-1154. http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a2/