Geodesic
The second coordinate sequence of a linear recurrence of maximum period over ring $\mathbb{Z}_{8}$
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 9-10.

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The analytical structure of the second coordinate in a linear recurrence sequence over ring $\mathbb{Z}_{8}$ is described. The lower bound of its rank (linear complexity) is specified. The class of polynomials and recurrences of the maximum period with the highest possible rank is found.
Keywords: linear recurring sequence, coordinate sequence, rank, analytical structure. 
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D. N. Bylkov. The second coordinate sequence of a linear recurrence of maximum period over ring $\mathbb{Z}_{8}$. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 9-10. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a2/

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[2] Helleseth T., Martinsen H. M., “Binary sequences of period $2^m-1$ with large linear complexity”, Information and Computation, 151 (1999), 73–91 | DOI | MR

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