Geodesic
Boolean functions generated by the most significant bits of linear recurrent sequences
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 59-60

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The class of Boolean functions generated by the most significant bits of linear recurrent sequences over the ring $\mathbb Z_{2^n}$ with a marked characteristic polynomial is considered. For these functions, their degree of nonlinearity is researched. It is proved that the class contains functions which are close to some bent functions.
Keywords: linear recurrent sequences, most significant bit sequences, Boolean functions, degree of nonlinearity. 
D. N. Bylkov. Boolean functions generated by the most significant bits of linear recurrent sequences. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 59-60. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a25/
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[1] Bylkov D. N., Kamlovskii O. V., “Parametry bulevykh funktsii, postroennykh s ispolzovaniem starshikh koordinatnykh posledovatelnostei lineinykh rekurrent”, Matem. vopr. kriptogr., 3:4 (2012), 25–53

[2] Kurakin V. L., Kuzmin A. S., Mikhalev A. V., Nechaev A. A., “Linear recurring sequences over rings and modules”, J. Math. Sci. (New York), 76:6 (1995), 2793–2915 | DOI | MR | Zbl