On binary digit-position sequences over Galois rings, admitting an effect of reduction of period
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 1, pp. 223-230.

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A class of binary digit-position sequences, obtained from the linear recurring sequence of maximal period over Galois rings of odd characteristics and admitting an effect of twofold reduction of period, has been found. A condition was found when sequences of some fixed linear recurring sequence of maximal period over Galois fields with such property are exhausted only by that class.
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S. A. Kuzmin. On binary digit-position sequences over Galois rings, admitting an effect of reduction of period. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 1, pp. 223-230. http://geodesic.mathdoc.fr/item/FPM_2015_20_1_a11/

[1] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, v. 2, Gelios ARV, M., 2003

[2] Kamlovskii O. V., Kuzmin A. S., “Otsenki chastot poyavleniya elementov v lineinykh rekurrentnykh posledovatelnostyakh nad koltsami Galua”, Fundament. i prikl. matem., 6:4 (2000), 1083–1094 | MR | Zbl

[3] Kuzmin A. S., “O periodakh razryadov v $r$-ichnoi sisteme schisleniya znakov lineinykh rekurrentnykh posledovatelnostei nad konechnymi prostymi polyami”, Bezopasn. inform. tekhnol., 1995, no. 4, 71–75 | MR

[4] Kuzmin A. S., Marshalko G. B., Nechaev A. A., “Vosstanovlenie lineinoi rekurrentnoi posledovatelnosti na primarnym koltsom vychetov po eë uslozhneniyu”, Matem. vopr. kriptogr., 1:2 (2010), 31–56

[5] Nechaev A. A., “Kod Kerdoka v tsiklicheskoi forme”, Diskret. matem., 1:4 (1989), 123–139 | MR | Zbl

[6] V. N. Sachkov (Red.), Trudy po diskretnoi matematike, 1, TVP, M., 1997 | MR | Zbl