Geodesic
The second coordinate sequence of the MP-LRS over nontrivial Galois ring of an odd characteristic
Diskretnaya Matematika, Tome 28 (2016) no. 1, pp. 123-149

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A Galois ring is said to be nontrivial if it is neither a field, nor a residue ring. Divisors and multiples of the minimal polynomial of the second $p$-adic coordinate sequence of a linear recurrent sequence of maximum period (MP LRS) over a nontrivial Galois ring of an odd characteristic are described, as well as their relation to the initial vector of the LRS. As a corollary, nontrivial upper and lower bounds for the rank of the second coordinate sequence of a MP LRS over a nontrivial Galois ring of an odd characteristic are obtained.
Keywords: Galois ring, linear recurrent sequence, coordinate sequence, bound for the rank. 
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     author = {V. N. Tsypyschev},
     title = {The second coordinate sequence of the {MP-LRS} over nontrivial {Galois} ring of an odd characteristic},
     journal = {Diskretnaya Matematika},
     pages = {123--149},
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     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_1_a7/}
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V. N. Tsypyschev. The second coordinate sequence of the MP-LRS over nontrivial Galois ring of an odd characteristic. Diskretnaya Matematika, Tome 28 (2016) no. 1, pp. 123-149. http://geodesic.mathdoc.fr/item/DM_2016_28_1_a7/